A159598 - OEIS

%I #2 Mar 30 2012 18:37:17

%S 1,1,9,52,389,3741,49908,938799,25477165,984680146,54180019253,

%T 4211350678751,462028240134476,71561459522839253,15611478225943599423,

%U 4816139618587302209166,2092942812095475521879845

%N 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.

%F 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.

%e G.f.: A(x) = 1 + x + 9*x^2 + 52*x^3 + 389*x^4 + 3741*x^5 +...

%e log(A(x)) = Sum_{n>=1} [x + 2^(n+2)*x^2 + 3^(n+2)*x^3 +...]^n/n.

%e D^n x(1+x)/(1-x)^2 = x + 2^(n+2)*x^2 + 3^(n+2)*x^3 + 4^(n+2)*x^4 +...

%o (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)}

%Y Cf. A156170, A159596, A159597.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 05 2009