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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.
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%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