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%I #4 Mar 31 2012 13:19:58
%S 1,1,1,2,5,1,5,22,9,1,14,93,58,13,1,42,386,325,110,17,1,132,1586,1686,
%T 765,178,21,1,429,6476,8330,4746,1477,262,25,1,1430,26333,39796,27314,
%U 10654,2525,362,29,1,4862,106762,185517,149052,69930,20754
%N A triangle related to A000108 (Catalan) and A000302 (powers of 4).
%F a(n, m) = binomial(n, m-1)*(4^(n-m+1)-binomial(2*n, n)/binomial(2*(m-1), m-1))/2, n >= m >= 0. G.f. for column m: c(x)*(x/(1-4*x))^m, where c(x) = g.f. for Catalan numbers (A000108).
%Y The m=0..6 column sequences are: A000108, A000346, A018218, A042941, A042985, A045505, A045622. Row sums: A046814.
%K easy,nonn,tabl
%O 0,4
%A _Wolfdieter Lang_
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