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

1, 2, 5, 16, 63, 288, 1461, 8013, 46896, 290916, 1905162, 13131193, 95005565, 719862361, 5700083435, 47075439047, 404760508374, 3617018777976, 33539368302476, 322222320833572, 3202873385842352, 32895350423011349

Offset: 0

Author

Paul D. Hanna, Nov 03 2006

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A124469, A124460.

Programs

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)}