A124463 Row 3 of rectangular table A124460.
1, 4, 13, 44, 162, 637, 2622, 11188, 49293, 223768, 1044661, 5006126, 24580704, 123464593, 633467893, 3315948760, 17690431736, 96101620364, 531196784996, 2985589206506, 17053375055317, 98942675518256, 582858713958087
Offset: 0
Keywords
Programs
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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]}
Formula
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.