A094526 Square array of binomial transforms read by antidiagonals.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 13, 5, 1, 1, 6, 21, 34, 21, 6, 1, 1, 7, 31, 73, 73, 31, 7, 1, 1, 8, 43, 136, 185, 136, 43, 8, 1, 1, 9, 57, 229, 381, 381, 229, 57, 9, 1, 1, 10, 73, 358, 685, 826, 685, 358, 73, 10, 1, 1, 11, 91, 529, 1121, 1531

Offset: 0

Author

Paul Barry, May 07 2004

Keywords

• easy
• nonn
• tabl

Comments

Rows (and columns) are binomial transforms of [1,k,k(k-1),k(k-1)(k-2),0,0,...], k>=0. One of a family of arrays that converge to A088699.

Examples

			Rows start
1,1,1,1,1,...
1,2,3,4,5,...
1,3,7,13,21,...
1,4,13,34,73,...
1,5,21,73,185,...
		

Crossrefs

Cf. A094525.

Formula

Square array T(n, k) defined by T(n, k)=1+kn+k(k-1)n(n-1)/2+k(k-1)(k-2)n(n-1)(n-2)/6