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%I #5 Dec 26 2023 13:06:01
%S 1,2,0,3,2,0,4,6,4,0,5,12,16,9,0,6,20,40,45,21,0,7,30,80,135,126,51,0,
%T 8,42,140,315,441,357,127,0,9,56,224,630,1176,1428,1016,323,0,10,72,
%U 336,1134,2646,4284,4572,2907,835,0
%N Triangle read by rows, A007318 * (A129186 * (A001006 * 0^(n-k))).
%C Row sums = the Catalan numbers, A000108, starting with offset 1:
%C (1, 2, 5, 14, 42,...).
%F Triangle read by rows, A007318 * (A129186 * (A001006 * 0^(n-k)))
%F Binomial transform of a bidiagonal matrix with (1,0,0,0,..,.) as the main
%F diagonal and A001006 as the subddiagonal starting (1, 2, 4, 9, 21, 51,...).
%e First few rows of the triangle =
%e 1;
%e 2, 0;
%e 3, 2, 0;
%e 4, 6, 4, 0;
%e 5, 12, 16, 9, 0;
%e 6, 20, 40, 45, 21, 0;
%e 7, 30, 80, 135, 126, 51, 0;
%e 8, 42, 140, 315, 441, 357, 127, 0;
%e 9, 56, 224, 630, 1176, 1428, 1016, 323, 0;
%e 10, 72, 336, 1134, 2646, 4284, 4572, 2907, 835, 0;
%e 11, 90, 480, 1890, 5292, 10710, 15240, 14535, 8350, 2188;
%e 12, 110, 660, 2970, 9702, 23562, 41910, 53295, 45925, 24068, 5798;
%e ...
%Y Cf. A001006, A000108
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Jan 11 2009
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