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

Author

Philippe Deléham, Sep 17 2005

Keywords

• nonn
• tabl

Examples

			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.