%I #11 Mar 22 2016 20:21:03
%S 1,0,0,0,1,0,0,1,1,0,0,2,2,2,0,0,5,4,4,5,0,0,14,10,9,10,14,0,0,42,28,
%T 23,23,28,42,0,0,132,84,65,60,65,84,132,0,0,429,264,196,171,171,196,
%U 264,429,0,0,1430,858,618,518,490,518,618,858,1430,0
%N Table T(n,k), n>=0, k>=0, product M*M^(T) where M is the lower triangular matrix in A106566 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, 2, 2, 1, 0, 0, 0, 0, ...
%e 0, 5, 5, 3, 1, 0, 0, 0, ...
%e ...
%e Matrix M^(T):
%e 1, 0, 0, 0, 0, 0, ...
%e 0, 1, 1, 2, 5, 14, ...
%e 0, 0, 1, 2, 5, 14, ...
%e 0, 0, 0, 1, 3, 9, ...
%e 0, 0, 0, 0, 1, 4, ...
%e 0, 0, 0, 0, 0, 1, ...
%e ...
%e Table begins:
%e 1, 0, 0, 0, 0, 0, 0, ...
%e 0, 1, 1, 2, 5, 14, ...
%e 0, 1, 2, 4, 10, 28, ...
%e 0, 2, 4, 9, 23, 65, ...
%e 0, 5, 10, 23, 60, ...
%e 0, 14, 28, 65, 171, ...
%e 0, 42, 84, 196, ...
%Y Diagonal sums : 1, 0, 1, 2, 6, 18, 57, 186, 622, 2120, ... see A000957.
%K nonn,tabl
%O 0,12
%A _Philippe Deléham_, Sep 17 2005