A124532 Row 2 of rectangular table A124530.

1, 1, 3, 10, 39, 174, 858, 4564, 25793, 153301, 951325, 6130757, 40861658, 280767621, 1983859580, 14385651988, 106878699675, 812480791324, 6312686006725, 50083418434737, 405430892640225, 3346568909331984

Offset

0,3

Comments

In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(2n), where R_n(x) is the g.f. of row n in table A124530.

Prog

(PARI) a(n)=local(R); R=vector(n+3, r, vector(n+3, c, if(r==1 || c<=2, 1, r^(c-2)))); for(i=0, n, for(r=0, n, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^(r*c)+O(x^(n+1)))))); R[3][n+1]

Crossrefs

Cf. A124530 (table); other rows: A124531, A124533, A124534, A124535, A124536.

Sequence in context: A205543 A137590 A352174 * A343795 A305560 A074728

Adjacent sequences: A124529 A124530 A124531 * A124533 A124534 A124535

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2006

Status

approved