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%I #8 May 10 2013 12:45:06
%S 1,1,1,1,2,2,1,3,5,5,1,4,10,14,14,1,5,17,35,42,42,1,6,26,74,126,132,
%T 132,1,7,37,137,326,462,429,429,1,8,50,230,726,1446,1716,1430,1430,1,
%U 9,65,359,1434,3858,6441,6435,4862,4862,1,10,82,530,2582,8952,20532,28770
%N Square array read by antidiagonals in which row n has g.f. C/(1-n*x*C) where C = (1/2-1/2*(1-4*x)^(1/2))/x = g.f. for Catalan numbers A000108.
%F a(n, m) = 1/(m+1)*Sum_{k=0..m} binomial(2*m-k, m)*(k+1)*(n-m)^k, m=0..n.
%e Array begins
%e 1 1 2 5 14 42 ... (n=0)
%e 1 2 5 14 42 132 ... (n=1)
%e 1 3 10 35 126 ... (n=2)
%e 1 4 17 74 326 ...
%Y Rows give A000108, A000108, A001700, A049027, A076025, A076026. Cf. A076037, A067347.
%Y Cf. A059718.
%K nonn,tabl
%O 0,5
%A _N. J. A. Sloane_, Oct 29 2002
%E More terms from _Vladeta Jovovic_, Jul 18 2003
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