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%I #3 Mar 30 2012 18:37:01
%S 1,4,13,44,162,637,2622,11188,49293,223768,1044661,5006126,24580704,
%T 123464593,633467893,3315948760,17690431736,96101620364,531196784996,
%U 2985589206506,17053375055317,98942675518256,582858713958087
%N Row 3 of rectangular table A124460.
%F G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^3, where R_n(x) is the g.f. of row n in table A124460 and satisfies: R_n(x) = Sum_{k>=0} x^k * R_k(x)^n for n>=0.
%o (PARI) {a(n)=local(m=max(n,3),R=vector(m+1,r,vector(m+1,c,binomial(r+c-2,c-1)))); for(i=0,m,for(r=0,m,R[r+1]=Vec(sum(c=0,m,x^c*Ser(R[c+1])^r+O(x^(m+1))))));R[4][n+1]}
%Y Cf. A124460 (table); other rows: A124461, A124462, A124464, A124465, A124466.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 03 2006
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