A124549 Derived from a diagonal of rectangular table A124540: a(n) = A124540(n+1,n)/(n+1).

1, 1, 5, 39, 399, 4943, 70846, 1142543, 20355695, 395414964, 8292073877, 186265497096, 4453789285009, 112771923093955, 3010597702761965, 84424863975107571, 2478907364772699611, 75998810193380960765

Offset

0,3

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.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = A124548(n)/(n+1).

Prog

(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]/(n+1)

Crossrefs

Cf. A124540, A124548, A124547.

Sequence in context: A215506 A316654 A070767 * A308939 A317618 A024216

Adjacent sequences: A124546 A124547 A124548 * A124550 A124551 A124552

Keyword

nonn

Author

Paul D. Hanna, Nov 05 2006

Status

approved