



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
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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/(1x)))^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/(1x); CoefficientList[Series[1/(1y 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



