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

0,2

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.

Links

Table of n, a(n) for n=0..24.

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.

Prog

(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]}

Crossrefs

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

Sequence in context: A129698 A261134 A117419 * A026898 A088930 A225588

Adjacent sequences: A124458 A124459 A124460 * A124462 A124463 A124464

Keyword

nonn

Author

Paul D. Hanna, Nov 03 2006

Status

approved