A096583 Symmetric square array T(n,k)=T(k,n), read by antidiagonals, such that the n-th diagonal equals the convolution of the n-th row with the antidiagonal sums, with T(0,n)=1, for n>=0.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 8, 7, 1, 1, 9, 16, 16, 9, 1, 1, 11, 23, 20, 23, 11, 1, 1, 13, 35, 44, 44, 35, 13, 1, 1, 15, 46, 69, 44, 69, 46, 15, 1, 1, 17, 62, 99, 108, 108, 99, 62, 17, 1, 1, 19, 77, 147, 179, 96, 179, 147, 77, 19, 1, 1, 21, 97, 206, 272, 248, 248, 272, 206, 97, 21

Offset: 0

Author

Paul D. Hanna, Jun 28 2004

Keywords

• nonn
• tabl

Comments

The main diagonal (A096585) equals the partial sums of the antidiagonal sums (A096584).

Examples

			Antidiagonal sums are A096584 =
[1,2,5,12,24,52,90,186,306,574,...];
convolution of antidiagonal sums and first row yields main diagonal:
A096585 = [1,3,8,20,44,96,186,372,678,...];
convolution of antidiagonal sums and second row yields secondary
diagonal:
[1,5,16,44,108,248,530,1088,2138,4068,...].
Rows begin:
[1,1,1,1,1,1,1,1,1,...],
[1,3,5,7,9,11,13,15,17,...],
[1,5,8,16,23,35,46,62,77,...],
[1,7,16,20,44,69,99,147,206,...],
[1,9,23,44,44,108,179,272,379,...],
[1,11,35,69,108,96,248,429,669,...],
[1,13,46,99,179,248,186,530,965,...],
[1,15,62,147,272,429,530,372,1088,...],
[1,17,77,206,379,669,965,1088,678,...],...
		

Crossrefs

Cf. A096584, A096585.

Programs

PARI

T(n,k)=if(n<0 || k<0,0,if(n==0 || k==0,1,if(n>k, sum(j=0,k,T(n-k,j)*sum(i=0,k-j,T(k-j-i,i))), sum(j=0,n,T(k-n,j)*sum(i=0,n-j,T(n-j-i,i))););))