A124547 Main diagonal of rectangular table A124540.

1, 1, 7, 73, 939, 13976, 233241, 4282895, 85445683, 1834958107, 42110641373, 1026677317227, 26462793170760, 718141884712500, 20446913056248836, 608923223179959780, 18917094810892717955, 611616504412815339432

Offset: 0

Author

Paul D. Hanna, Nov 05 2006

Keywords

• nonn

Comments

In table A124540, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = [ Sum_{k>=0} y^k*R_k(y)^n ]^n for n>=0.

Crossrefs

Cf. A124540, A124548, A124549.

Programs

PARI

a(n)=local(R);R=vector(n+1,r,vector(n+1,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)))))); Vec(Ser(R[n+1])^n+O(x^(n+1)))[n+1]