A110855 Table T(n,k), n >= 0, k >= 0, product M*M^(T) where M is the lower triangular matrix in A048993 (Stirling2 numbers) and M^(T) denotes the transpose matrix of M, read by antidiagonals.

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 4, 4, 1, 0, 0, 1, 8, 11, 8, 1, 0, 0, 1, 16, 28, 28, 16, 1, 0, 0, 1, 32, 71, 87, 71, 32, 1, 0, 0, 1, 64, 184, 266, 266, 184, 64, 1, 0, 0, 1, 128, 491, 823, 952, 823, 491, 128, 1, 0, 0, 1, 256, 1348, 2598, 3381, 3381

Offset

0,13

Links

Table of n, a(n) for n=0..72.

Example

Matrix M:
  1, 0, 0, 0, 0, 0, 0, 0, ...
  0, 1, 0, 0, 0, 0, 0, 0, ...
  0, 1, 1, 0, 0, 0, 0, 0, ...
  0, 1, 3, 1, 0, 0, 0, 0, ...
  0, 1, 7, 6, 1, 0, 0, 0, ...
  ...
Matrix M^(T):
  1, 0, 0, 0, 0,  0, ...
  0, 1, 1, 1, 1,  1, ...
  0, 0, 1, 3, 7, 15, ...
  0, 0, 0, 1, 6, 25, ...
  0, 0, 0, 0, 1, 10, ...
  0, 0, 0, 0, 0,  1, ...
  ...
Table begins:
  1, 0,   0,   0,   0,   0,   0,   0,   0, 0, 0, ...
  0, 1,   1,   1,   1,   1,   1,   1,   1, 1,
  0, 1,   2,   4,   8,  16,  32,  64, 128, ...
  0, 1,   4,  11,  28,  71, 184, 491, ...
  0, 1,   8,  28,  87, 266, 823, ...
  0, 1,  16,  71, 266, 952, ...
  0, 1,  32, 184, 823, ...
  0, 1,  64, 491, ...
  0, 1, 128, ...
  0, 1, ...
  0, ...

Crossrefs

Diagonal sums: 1, 0, 1, 2, 4, 10, 29, 90, 295, ... see A000995.

Main diagonal: 1, 1, 2, 11, 87, 952, 13513, ... see A047797.

Sequence in context: A055363 A363845 A350681 * A054673 A155103 A295819

Adjacent sequences: A110852 A110853 A110854 * A110856 A110857 A110858

Keyword

nonn,tabl

Author

Philippe Deléham, Sep 17 2005

Status

approved