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A124470 Row sums of the triangle A124469, in which row n equals the inverse binomial transform of column n in the triangle A124460.

%I A124470 #3 Mar 30 2012 18:37:01
%S A124470 1,2,5,16,63,288,1461,8013,46896,290916,1905162,13131193,95005565,
%T A124470 719862361,5700083435,47075439047,404760508374,3617018777976,
%U A124470 33539368302476,322222320833572,3202873385842352,32895350423011349
%N A124470 Row sums of the triangle A124469, in which row n equals the inverse binomial transform of column n in the triangle A124460.
%C A124470 In table A124460, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k * R_k(y)^n for n>=0.
%o A124470 (PARI) {a(n)=local(R=vector(n+2,r,vector(n+2,c,binomial(r+c-2,c-1)))); for(i=0,n,for(r=0,n,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^r+O(x^(n+1)))))); subst(truncate(subst(Ser(vector(n+1,j,R[j][n+1])),x,x/(1+x))/(1+x)),x,1)}
%Y A124470 Cf. A124469, A124460.
%K A124470 nonn
%O A124470 0,2
%A A124470 _Paul D. Hanna_, Nov 03 2006