login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127954 Triangle, A097805 * A127648. 1
1, 0, 2, 0, 2, 3, 0, 2, 6, 4, 0, 2, 9, 12, 5, 0, 2, 12, 24, 20, 6, 0, 2, 15, 40, 50, 30, 7, 0, 2, 18, 60, 100, 90, 42, 8, 0, 2, 21, 84, 175, 210, 147, 56, 9, 0, 2, 24, 112, 280, 420, 392, 224, 72, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums = A045623 starting (1, 2, 5, 12, 28, 64, ...).

Dropping the first column gives A128710. - Peter Bala, Mar 05 2013

T(n,k) is the number of ways to place n unlabeled balls into 2 boxes, make compositions of the integer number of balls in each box so that the total number of parts in both compositions is k. - Geoffrey Critzer, Sep 21 2013

LINKS

Table of n, a(n) for n=1..55.

FORMULA

A097805 * A127648 as infinite lower triangular matrices.

E.g.f.: 1/(1 - y*(x/(1-x)))^2. - Geoffrey Critzer, Sep 21 2013

EXAMPLE

First few rows of the triangle are:

1;

0, 2;

0, 2, 3;

0, 2, 6, 4;

0, 2, 9, 12, 5;

0, 2, 12, 24, 20, 6;

0, 2, 15, 40, 50, 30, 7;

...

T(4,3)=12. Place 4 unlabeled balls into 2 labeled boxes then make compositions of the integer number of balls in each box so that there are a total of 3 parts.

/**** 3 ways since there are 3 compositions of 4 into 3 parts.

*/***  2 ways 1;1+2  and 1;2+1

**/**  2 ways 2;1+1  and 1+1;2.

***/*  2 ways as above.

****/  3 ways as above.

3+2+2+2+3=12. - Geoffrey Critzer, Sep 21 2013

MATHEMATICA

nn=10; a=x/(1-x); CoefficientList[Series[1/(1-y a)^2, {x, 0, nn}], {x, y}]//Grid (* Geoffrey Critzer, Sep 21 2013 *)

CROSSREFS

Cf. A097805, A127648, A128710.

Sequence in context: A198632 A060155 A209127 * A198061 A265583 A238156

Adjacent sequences:  A127951 A127952 A127953 * A127955 A127956 A127957

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Feb 09 2007

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 July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)