A124533 Row 3 of rectangular table A124530.

1, 1, 4, 16, 71, 351, 1891, 10888, 66139, 420235, 2775981, 18978873, 133828922, 970678790, 7226115267, 55115404005, 430080085093, 3429311454089, 27912555377062, 231710034354364, 1960247357996533, 16889105788701591

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, A124532, A124534, A124535, A124536.

Programs

PARI

a(n)=local(R);R=vector(n+4,r,vector(n+4,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[4][n+1]

Formula

G.f.: A(x) = Sum_{n>=0} x^n*R_n(x)^(3n), where R_n(x) is the g.f. of row n in table A124530.