|
%I #14 Jan 25 2020 18:26:49
%S 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,
%T 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,
%U 128,491,823,952,823,491,128,1,0,0,1,256,1348,2598,3381,3381
%N 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.
%e Matrix M:
%e 1, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 1, 0, 0, 0, 0, 0, 0, ...
%e 0, 1, 1, 0, 0, 0, 0, 0, ...
%e 0, 1, 3, 1, 0, 0, 0, 0, ...
%e 0, 1, 7, 6, 1, 0, 0, 0, ...
%e ...
%e Matrix M^(T):
%e 1, 0, 0, 0, 0, 0, ...
%e 0, 1, 1, 1, 1, 1, ...
%e 0, 0, 1, 3, 7, 15, ...
%e 0, 0, 0, 1, 6, 25, ...
%e 0, 0, 0, 0, 1, 10, ...
%e 0, 0, 0, 0, 0, 1, ...
%e ...
%e Table begins:
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e 0, 1, 2, 4, 8, 16, 32, 64, 128, ...
%e 0, 1, 4, 11, 28, 71, 184, 491, ...
%e 0, 1, 8, 28, 87, 266, 823, ...
%e 0, 1, 16, 71, 266, 952, ...
%e 0, 1, 32, 184, 823, ...
%e 0, 1, 64, 491, ...
%e 0, 1, 128, ...
%e 0, 1, ...
%e 0, ...
%Y Diagonal sums: 1, 0, 1, 2, 4, 10, 29, 90, 295, ... see A000995.
%Y Main diagonal: 1, 1, 2, 11, 87, 952, 13513, ... see A047797.
%K nonn,tabl
%O 0,13
%A _Philippe Deléham_, Sep 17 2005
|
