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A159597 G.f.: A(x) = exp( Sum_{n>=1} [ D^n x/(1-x)^3 ]^n/n ), where differential operator D = x*d/dx.

%I A159597 #2 Mar 30 2012 18:37:17
%S A159597 1,1,7,37,245,2094,24661,410376,9809637,334520167,16192227784,
%T A159597 1107914634442,106788033119369,14525652771018918,2780328926392863928,
%U A159597 751651711717655433750,286240041470280077141769
%N A159597 G.f.: A(x) = exp( Sum_{n>=1} [ D^n x/(1-x)^3 ]^n/n ), where differential operator D = x*d/dx.
%F A159597 G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^n*k(k+1)/2*x^k]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k.
%e A159597 G.f.: A(x) = 1 + x + 7*x^2 + 37*x^3 + 245*x^4 + 2094*x^5 +...
%e A159597 log(A(x)) = Sum_{n>=1} [x + 2^n*3*x^2 + 3^n*6*x^3 +...]^n/n.
%e A159597 D^n x/(1-x)^3 = x + 2^n*3*x^2 + 3^n*6*x^3 + 4^n*10*x^4 +...
%o A159597 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,sum(k=1,n,k^m*k*(k+1)/2*x^k+x*O(x^n))^m/m)));polcoeff(A,n)}
%Y A159597 Cf. A156170, A159596, A159598.
%K A159597 nonn
%O A159597 0,3
%A A159597 _Paul D. Hanna_, May 05 2009