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# User:Yahia Kahloune

Ingénieur en retraite ,passionné par les mathématiques et particulièrement l'analyse combinatoire.

```A229026 : Expansion of  1/((1-x)(1-5x)(1-5x)(1-8x))
```

``` 1 19 238 2490 23631 211509 1823908 15348100 127057261 1040261799
8453319978  .......
```

``` a(n)=[2*8^(n+4)-(5^(n+2))*(84*n+287)-9]/1008
```

``` a(0)=1
a(1)=19
a(2)=238
```

```        Expansion of  1/((1-x)(1-4x)(1-5x)(1-7x))
```
```    A021754   : 1 17 190 1770 14931 118587 905920  .......
```

Formule: a(n)=[2*7^(n+3)-9*5^(n+3)+8*4^(n+3)-1]/72

```    a(0)=1
a(1)=17
a(2)=190
```

```          Expansion of   1/((1-x)(1-3x)(1-5x)(1-6x))
```
```     A021414  :  1 15 148 1218 9079 63693 42946    ..........
```
```     Formule :  a(n)=[8*6^(n+3)-15*5^(n+3)+10*3^(n+3))-3]/120
```
```        a(0)=1
a(1)=15
a(3)=148
```

```        Expansion of 1/((1-x)(1-4x)(1-5x)(1-6x))
```
```    A021744 :     1 16 167 1442 11193 81228 563179  ......
```
```   Formule : a(n)=[6^(n+4)-3*5^(n+4)+10*4^(n+3)-1]/60
```
```   a(0)=1
a(1)=16
a(2)=167
```

```              Expansion 0f  1/((1-x)(1-3x)(1-7x)).
```
```     A016212 : 1 11 90 670 4811 34041 239380 .....
```

Formule: a(n)=[ 7^(n+2)-3^(n+3)+2]/24 .

``` a(0)=1.     a(1)=11.    a(2)=90.
```

```  Expansion of 1/((1-x)(1-3x)(1-8x)).
```

A016214 : 1 12 109 912 7417 59700 478693 .....

```Formule: a(n)=[ 2*8^(n+2)-7*3^(n+2)+5]/70 .
```
```a(0)=1.    a(1)=12.    a(2)=109.
```

```    Expansion of 1/((1-x)(1-6x)(1-8x)).
```
```A016243:  1 15 163 1563 14059 121803 1030411  .....
```

Formule: a(n)=[ 5*8^(n+2)-7*6^(n+2)+2]/70 .

```a(0)=1.    a(1)=15.    a(2)=163.
```

```    Expansion of  1/((1-x)(1-x)(1-2x)(1-4x)).
```
```A227209 :1 8 43 198 849 3516 14311 57746 231997 ...
```
```Formule: a(n)= [ 4^(n+3)-9*2^(n+3)+6*n+26]/18 .
```
```a(0)=1.     a(1)=8.     a(2)=43.
```

```Expansion:A021414:
```

a(n)=[ 8*6^(n+3)-15*5^(n+3)+10*3^(n+3)-3]/120.

``` Expansion of  1/((1-2x)(1-5x)(1-7x)(1-8x))
```
```A025992  :1 22 313 3666 38493 377286 ......
```

Formule:a(n)=[ 5*8^(n+3)-9*7^(n+3)+5^(n+4)-2^(n+3)]/90.

```  a(o)=1.     a(1)=22   a(2)=313.
```

```     Expansion  of      1/((1-4x)(1-4x)(1-8x)).
```
```     A0------:  1 16 176 1664 14592 122880 1011712 8224768  ......
```
```     Formule:  a(n)=[8^(n+2)-(n+3)*4^(n+2)]/16.
```
```     a(0)=1.     a(1)=16.     a(2)=176.
```

```     Expansion  of   1/((1-x)(1-2x)(1-8x)).
```
```     A016203  :   1 11 95 775 6231 49911 399415   ......
```
```     Formule:  a(n)=[ 4*8^(n+1)-7*2^(n+1)+3 ]/21  .
```
```     a(0)=1.     a(1)=11.     a(3)=95.
```

```    Expansion of    1/((1-x)(1-3x)(1-6x)(1-8x)).
```
```    A021503  :   1 18 217 2214 20701 183906 1582129   ......
```
```    Formule :  a(n)=[ 3*8^(n+3)-7*6^(n+3)-7*3^(n+3) -3]/210.
```
```    a(0)=1.     a(1)=18.     a(2)=217.
```

```    Expansion   of    1/((1-4x)(1-4x)(1-8x)).
A225397: 1 16 176 1664 14592 122880 1011712 8224768 66387968 533725184 4281335808
```
```   Formule: a(n)=(8^(n+2)-(n+3)*4^(n+2))/16.
```
```   a(0)=1.    a(1)=16.    a(2)=176.
```
```   cette suite existe dans les commentaires de  A0209200.
```

```  A019512 :Expansion of  1/((1-4x)(1-7x)(1-8x)).
a(0)=1, a(1)=19, a(2)=245;  a(n)=(3*8^(n+2)-4*7^(n+2)+4^(n+2))/12.  From Yahia Kahloune, May 07 2013.
```

```  A021814.   Expansion of  1/((1-x)(1-4x)(1-6x)(1-8x)).
Formula: a(0)=1, a(1)=19, a(2)=239; a(n)=(15*8^(n+3)-42*6^(n+3)+35*4^(n+3)-8)/840.From Yahia Kahloune,
May 07 2013.

A025933: Expansion of 1/(1-2x)(1-3x)(1-5x)(1-9x)).
Formula: a(0)=1, a(1)=19, a(2)=240; a(n)=(9^(n+3)-7*5^(n+3)+14*3^(n+3)-8*2^(n+3)))/168. From Yahia Kahloune, May 08 213.

A025927 :Expansion of 1/((1-2x)(1-3x)(1-4x)(1-10x)).
a(0)=1, a(1)=19, a(2)=245; a(n)=( 10^(n+3)-7*4^(n+4)+16*3^(n+4)-21*2^(n+3))/336. From yahia Kahloune, May 09 2013.

```

```Expansion of  1/((1-x)(1-5x)(1-5x)(1-8x))
```

```1 19 238 2490 23631 211509 1823908 15348100 127057261 1040261799
8453319978  .......
```

```a(n)=[2*8^(n+4)-(5^(n+2))*(84*n+287)-9]/1008
```

```a(0)=1
a(1)=19
a(2)=238
```

```       Expansion of  1/((1-x)(1-4x)(1-5x)(1-7x))
A021754   : 1 17 190 1770 14931 118587 905920  .......
```

Formule: a(n)=[2*7^(n+3)-9*5^(n+3)+8*4^(n+3)-1]/72

```   a(0)=1
a(1)=17
a(2)=190
```

```         Expansion of   1/((1-x)(1-3x)(1-5x)(1-6x))
A021414  :  1 15 148 1218 9079 63693 42946    ..........
Formule :  a(n)=[8*6^(n+3)-15*5^(n+3)+10*3^(n+3))-3]/120
a(0)=1
a(1)=15
a(3)=148
```

```       Expansion of 1/((1-x)(1-4x)(1-5x)(1-6x))
A021744 :     1 16 167 1442 11193 81228 563179  ......
Formule : a(n)=[6^(n+4)-3*5^(n+4)+10*4^(n+3)-1]/60
a(0)=1
a(1)=16
a(2)=167
```

```             Expansion 0f  1/((1-x)(1-3x)(1-7x)).
A016212 : 1 11 90 670 4811 34041 239380 .....
```

Formule: a(n)=[ 7^(n+2)-3^(n+3)+2]/24 .

```a(0)=1.     a(1)=11.    a(2)=90.
```

``` Expansion of 1/((1-x)(1-3x)(1-8x)).
```

A016214 : 1 12 109 912 7417 59700 478693 .....

Formule: a(n)=[ 2*8^(n+2)-7*3^(n+2)+5]/70 . a(0)=1. a(1)=12. a(2)=109.

```   Expansion of 1/((1-x)(1-6x)(1-8x)).
```

A016243: 1 15 163 1563 14059 121803 1030411 ..... Formule: a(n)=[ 5*8^(n+2)-7*6^(n+2)+2]/70 .

a(0)=1. a(1)=15. a(2)=163.

```   Expansion of  1/((1-x)(1-x)(1-2x)(1-4x)).
```

A0----- :1 8 43 198 849 3516 14311 57746 231997 ... Formule: a(n)= [ 4^(n+3)-9*2^(n+3)+6*n+26]/18 . a(0)=1. a(1)=8. a(2)=43.

Expansion:A021414: a(n)=[ 8*6^(n+3)-15*5^(n+3)+10*3^(n+3)-3]/120.

```Expansion of  1/((1-2x)(1-5x)(1-7x)(1-8x))
```

A025992  :1 22 313 3666 38493 377286 ...... Formule:a(n)=[ 5*8^(n+3)-9*7^(n+3)+5^(n+4)-2^(n+3)]/90.

``` a(o)=1.     a(1)=22   a(2)=313.
```

```    Expansion  of      1/((1-4x)(1-4x)(1-8x)).
A0------:  1 16 176 1664 14592 122880 1011712 8224768  ......
Formule:  a(n)=[8^(n+2)-(n+3)*4^(n+2)]/16.
a(0)=1.     a(1)=16.     a(2)=176.
```

```    Expansion  of   1/((1-x)(1-2x)(1-8x)).
A016203  :   1 11 95 775 6231 49911 399415   ......
Formule:  a(n)=[ 4*8^(n+1)-7*2^(n+1)+3 ]/21  .
a(0)=1.     a(1)=11.     a(3)=95.
```

```   Expansion of    1/((1-x)(1-3x)(1-6x)(1-8x)).
A021503  :   1 18 217 2214 20701 183906 1582129   ......
Formule :  a(n)=[ 3*8^(n+3)-7*6^(n+3)-7*3^(n+3) -3]/210.
a(0)=1.     a(1)=18.     a(2)=217.
```

```   Expansion   of    1/((1-4x)(1-4x)(1-8x)).
A225397: 1 16 176 1664 14592 122880 1011712 8224768 66387968 533725184 4281335808
Formule: a(n)=(8^(n+2)-(n+3)*4^(n+2))/16.
a(0)=1.    a(1)=16.    a(2)=176.
cette suite existe dans les commentaires de  A0209200.
```

``` A019512 :Expansion of  1/((1-4x)(1-7x)(1-8x)).
a(0)=1, a(1)=19, a(2)=245;  a(n)=(3*8^(n+2)-4*7^(n+2)+4^(n+2))/12.  From Yahia Kahloune, May 07 2013.
```

``` A021814.   Expansion of  1/((1-x)(1-4x)(1-6x)(1-8x)).
Formula: a(0)=1, a(1)=19, a(2)=239; a(n)=(15*8^(n+3)-42*6^(n+3)+35*4^(n+3)-8)/840.From Yahia Kahloune,
May 07 2013.

A025933: Expansion of 1/(1-2x)(1-3x)(1-5x)(1-9x)).
Formula: a(0)=1, a(1)=19, a(2)=240; a(n)=(9^(n+3)-7*5^(n+3)+14*3^(n+3)-8*2^(n+3)))/168. From Yahia Kahloune, May 08 213.

A025927 :Expansion of 1/((1-2x)(1-3x)(1-4x)(1-10x)).
a(0)=1, a(1)=19, a(2)=245; a(n)=( 10^(n+3)-7*4^(n+4)+16*3^(n+4)-21*2^(n+3))/336. From yahia Kahloune, May 09 2013.
```

```A0225397
```

```Expansion of  1/((1-x)(1-5x)(1-5x)(1-8x))
```

```1 19 238 2490 23631 211509 1823908 15348100 127057261 1040261799
8453319978  .......
```

```a(n)=[2*8^(n+4)-(5^(n+2))*(84*n+287)-9]/1008
```

```a(0)=1
a(1)=19
a(2)=238

```

A028054 : Expansion of 1/((1-3x)(1-5x)(1-6x)(1-8x)). Formula: a(0)=1, a(1)=22, a(2)=309; a(n)=[ 8^(n+3)-5*6^(n+3)+5^(n+4)-3^(n+3) ]/30. From Yahia Kahloune, May 09 2013.

A016243 :Expansion of 1/((1-x)(1-6x)(1-8x)). Formula: a(0)=1, a(1)=15, a(2)=163; a(n)=( 5*8^(n+2)-7*6^(n+2)+2 )/70. From Yahia Kahloune ,May 09 2013.

A016214: Expansion of 1/((1-x)(1-3x)(1-8x)). Formula: a(0)=1, a(1)=12, a(2)=109; a(n)=( 2*8^(n+2)-7*3^(n+2)+5 )/70. From Yahia Kahloune , May 09 2013.

A021214 : Expansion of 1/((1-x)(1-2x)(1-6x)(1-12x)). Formula: a(0)=1, a(1)=21, a(2)=313; a(n)=[ 2*12^(n+3)-11*6^(n+3)+33*2^(n+3)-24 ]/1320. From Yahia Kahloune, May 11 2013.

A021229 : Expansion of 1/((1-x)(1-2x)(1-7x)(1-9x)). Formula: a(0)=1, a(1)=19, a(2)=248; a(n)=(15*9^(n+3)-28*7^(n+3)+48*2^(n+3)-35)/1680. From Yahia Kahloune, May 11 2013.

A017952: Expansion of 1/((1-3x)(1-6x)(1-10x)). Formula: a(0)=1, a(1)=19, a(2)=253; a(n)=(3*10^(n+2)-7*6^(n+2)+4*3^(n+2))/84. From Yahia Kahloune, May 15 2013.

A021464: Expansion of 1/((1-x)(1-3x)(1-5x)(1-10x)) . Formula: a(0)=1, a(1)=19, a(2)=248, a(n)=(8*10^(n+3)-63*5^(n+3)+90*3^(n+3)-35)/2520. From Yahia Kahloune May 16 2013.