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%I #6 Nov 18 2017 01:40:19
%S 1,1,3,28,365,6496,147127,4033408,130058777,4822981120,202225551371,
%T 9460961327104,488602134968389,27609977350868992,1694576741234926655,
%U 112258296102497099776,7983577042683934226993,606688287932557859356672
%N E.g.f. satisfies: A(x) = exp(x*exp(x*A(x)^3)).
%C More generally, if G(x) = exp(x*exp(x*G(x)^p)),
%C where G(x)^m = Sum_{n>=0} g(n,m)*x^n/n!,
%C then g(n,m) = Sum_{k=0..n} C(n,k) * m*(p*(n-k) + m)^(k-1) * k^(n-k).
%H G. C. Greubel, <a href="/A161605/b161605.txt">Table of n, a(n) for n = 0..355</a>
%F a(n) = Sum_{k=0..n} C(n,k) * (3*(n-k) + 1)^(k-1) * k^(n-k).
%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 365*x^4/4! +...
%t Flatten[{1, Table[Sum[Binomial[n, k]*(3*(n - k) + 1)^(k - 1)*k^(n - k), {k, 0, n}], {n, 1, 50}]}] (* _G. C. Greubel_, Nov 18 2017 *)
%o (PARI) {a(n)=sum(k=0,n,binomial(n,k)*(3*(n-k)+1)^(k-1)*k^(n-k))}
%o (PARI) {a(n)=local(A=1+x);for(i=0,n,A=exp(x*exp(x*A^3+O(x^n))));n!*polcoeff(A,n,x)}
%Y Cf. A161552, A161567.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 14 2009
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