login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A166341 Coefficients of recursive differential polynomial:p(x,3)=x*(x^2 + 10*x + 1)/(1 - x)^4;p(x, n) = x*D[p[x, n - 1], x] 0
1, 1, 1, 1, 10, 1, 1, 23, 23, 1, 1, 50, 138, 50, 1, 1, 105, 614, 614, 105, 1, 1, 216, 2367, 4912, 2367, 216, 1, 1, 439, 8397, 31483, 31483, 8397, 439, 1, 1, 886, 28264, 176314, 314830, 176314, 28264, 886, 1, 1, 1781, 91880, 903104, 2632034, 2632034, 903104 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:{1, 2, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600,...}

REFERENCES

Douglas C. Montgomery and Lynwood A. Johnson, Forecasting and Time Series Analysis, MaGraw-Hill, New York, 1976, page 91

LINKS

Table of n, a(n) for n=1..52.

FORMULA

p(x,0)= 1/(1 - x);

p(x,1)= x/(1 - x)^2;

p(x,2)= x*(1 + x)/(1 - x)^3;

p(x,3)= x*(x^2 + 10*x + 1)/(1 - x)^4;

p(x,n)= x*D[p[x, n - 1], x]

EXAMPLE

{1},

{1, 1},

{1, 10, 1},

{1, 23, 23, 1},

{1, 50, 138, 50, 1},

{1, 105, 614, 614, 105, 1},

{1, 216, 2367, 4912, 2367, 216, 1},

{1, 439, 8397, 31483, 31483, 8397, 439, 1},

{1, 886, 28264, 176314, 314830, 176314, 28264, 886, 1},

{1, 1781, 91880, 903104, 2632034, 2632034, 903104, 91880, 1781, 1},

{1, 3572, 291669, 4347456, 19481898, 31584408, 19481898, 4347456, 291669, 3572, 1}

MATHEMATICA

p[x_, 0] := 1/(1 - x);

p[x_, 1] := x/(1 - x)^2;

p[x_, 2] := x*(1 + x)/(1 - x)^3;

p[x_, 3] := x*(x^2 + 10*x + 1)/(1 - x)^4;

p[x_, n_] := p[x, n] = x*D[p[x, n - 1], x]

a = Table[CoefficientList[FullSimplify[ExpandAll[(1 - x)^(n + 1)*p[x, n]/x]], x], {n, 1, 11}];

Flatten[a]

Table[Apply[Plus, CoefficientList[FullSimplify[ExpandAll[(1 - x)^(n + 1)*p[x, n]/x]], x]], {n, 1, 11}];

CROSSREFS

A123125

Sequence in context: A143683 A146773 A202941 * A113280 A159041 A154979

Adjacent sequences:  A166338 A166339 A166340 * A166342 A166343 A166344

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Oct 12 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 18 00:43 EST 2022. Contains 350410 sequences. (Running on oeis4.)