A124548 Secondary diagonal of rectangular table A124540: a(n) = A124540(n+1,n).

1, 2, 15, 156, 1995, 29658, 495922, 9140344, 183201255, 3954149640, 91212812647, 2235185965152, 57899260705117, 1578806923315370, 45158965541429475, 1350797823601721136, 42141425201135893387, 1367978583480857293770

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, A124549, A124547.

Programs

PARI

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

Formula

a(n) is divisible by (n+1): a(n)/(n+1) = A124549(n).