A124461 Row 1 of rectangular table A124460; also equals the antidiagonal sums of table A124460.

1, 2, 4, 9, 23, 66, 210, 731, 2744, 10959, 46058, 202028, 919386, 4321837, 20916763, 103958935, 529512396, 2759340117, 14690668955, 79813438230, 442057104246, 2493917931493, 14320972817368, 83652035642564, 496769855224824

Offset: 0

Author

Paul D. Hanna, Nov 03 2006

Keywords

• nonn

Comments

In table A124460, the o.g.f. of row n, R_n(y), satisfies: R_n(y) = Sum_{k>=0} y^k * R_k(y)^n for n>=0.

Crossrefs

Cf. A124460 (table); other rows: A124462, A124463, A124464, A124465, A124466.

Programs

PARI

{a(n)=local(m=max(n,1),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[2][n+1]}

Formula

O.g.f.: A(x) = Sum_{n>=0} x^n*R_n(x) = Sum_{k>=0} x^k/(1 - x*R_k(x)), where R_n(x) is the o.g.f. of row n in table A124460.