A108456 Table read by antidiagonals: T(n,k) = number of partitions of (n,k) into pairs (i,j) with i>0, j>=0.

1, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 3, 4, 5, 0, 1, 3, 6, 7, 7, 0, 1, 4, 8, 12, 12, 11, 0, 1, 4, 10, 16, 21, 19, 15, 0, 1, 5, 12, 23, 31, 36, 30, 22, 0, 1, 5, 15, 28, 45, 55, 58, 45, 30, 0, 1, 6, 17, 37, 60, 84, 94, 92, 67, 42, 0, 1, 6, 20, 44, 80, 115, 147, 153, 140, 97, 56, 0, 1, 7, 23

Offset: 0

Author

Christian G. Bower, Jun 03 2005

Keywords

• nonn
• tabl

Comments

(a,b)+(x,y)=(a+x,b+y); unit is (0,0).

Examples

			1 0 0 0 0 ...
1 1 1 1 1 ...
2 2 3 3 4 ...
3 4 6 8 10 ...
5 7 12 16 23 ...
(3,2)=(2,2)+(1,0)=(2,1)+(1,1)=(2,0)+(1,2)=(1,2)+(1,0)+(1,0)=(1,1)+(1,1)+(1,0), so a(3,2)=6.
		

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A108461, A108455. Columns 0-1: A000041, A000070. Main diagonal: A108457.

Formula

Euler transform of table whose g.f. is x/((1-x)*(1-y)).