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%I #6 Mar 30 2012 16:49:31
%S 1,1,1,1,1,1,1,1,2,2,1,1,3,5,5,1,1,4,10,14,14,1,1,5,17,35,42,42,1,1,6,
%T 26,74,126,132,132,1,1,7,37,137,326,462,429,429,1,1,8,50,230,726,1446,
%U 1716,1430,1430,1,1,9,65,359,1434,3858,6441,6435,4862,4862,1,1,10,82
%N Square array read by antidiagonals in which row n has g.f. (1-(n-1)*x*C)/(1-n*x*C) where C = (1/2-1/2*(1-4*x)^(1/2))/x = g.f. for Catalan numbers A000108.
%e Array begins
%e 1 1 1 2 5 14 42 ... (n=0)
%e 1 1 2 5 14 42 132 ... (n=1)
%e 1 1 3 10 35 126 ... (n=2)
%e 1 1 4 17 74 326 ...
%o (PARI) C(x)=(1/2-1/2*(1-4*x)^(1/2))/x; D(x)=(1-(m-1)*x*C(x))/(1-m*x*C(x)); for(i=0,15, forstep(m=i,0,-1,print1(polcoeff(D(x),i-m),","));print()) (Klasen)
%Y Rows give A000108, A000108, A001700, A049027, A076025, A076026. Cf. A076038, A067347.
%K nonn,tabl
%O 0,9
%A _N. J. A. Sloane_, Oct 29 2002
%E More terms from Lambert Klasen (lambert.klasen(AT)gmx.de), Jan 12 2005
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