A124468 Secondary diagonal of rectangular table A124460.

1, 3, 13, 73, 506, 4117, 37703, 378529, 4106995, 47766886, 592228264, 7791350900, 108323265571, 1585742194947, 24364012940723, 391780319558565, 6577005078357973, 115010285695135090, 2090723838361780991

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. A124460 (table); rows: A124461, A124462, A124463, A124464, A124465, A124466; A124467 (diagonal).

Programs

PARI

{a(n)=local(R=vector(n+2,r,vector(n+1,c,binomial(r+c-2,c-1)))); for(i=0,n+1,for(r=0,n+1,R[r+1]=Vec(sum(c=0,n,x^c*Ser(R[c+1])^r+O(x^(n+2))))));R[n+2][n+1]}