A159598 G.f.: A(x) = exp( Sum_{n>=1} [ D^n x(1+x)/(1-x)^3 ]^n/n ), where differential operator D = x*d/dx.

1, 1, 9, 52, 389, 3741, 49908, 938799, 25477165, 984680146, 54180019253, 4211350678751, 462028240134476, 71561459522839253, 15611478225943599423, 4816139618587302209166, 2092942812095475521879845

Offset: 0

Author

Paul D. Hanna, May 05 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 9*x^2 + 52*x^3 + 389*x^4 + 3741*x^5 +...
log(A(x)) = Sum_{n>=1} [x + 2^(n+2)*x^2 + 3^(n+2)*x^3 +...]^n/n.
D^n x(1+x)/(1-x)^2 = x + 2^(n+2)*x^2 + 3^(n+2)*x^3 + 4^(n+2)*x^4 +...
		

Crossrefs

Cf. A156170, A159596, A159597.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,sum(k=1,n,k^(m+2)*x^k+x*O(x^n))^m/m)));polcoeff(A,n)}

Formula

G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^(n+2)*x^k]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k.