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

Author

Paul D. Hanna, Nov 05 2006

Keywords

• nonn

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.

Crossrefs

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

Programs

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]

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.