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

0,5

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.

Links

Table of n, a(n) for n=0..71.

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

Example

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.

Sequence in context: A114197 A108350 A086617 * A088699 A101515 A327913

Adjacent sequences: A094523 A094524 A094525 * A094527 A094528 A094529

Keyword

easy,nonn,tabl

Author

Paul Barry, May 07 2004

Status

approved