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%I #5 Jul 14 2014 02:06:01
%S 1,1,3,13,109,1241,18541,340495,7475721,191215729,5590994041,
%T 184086712151,6745657327069,272484296020249,12037353264295269,
%U 577681783128081871,29946086856245571601,1668620115204908947937,99516760157428436346481,6329149392153729480812839
%N E.g.f: A(x) = Sum_{n>=0} (1 + x*A(x)^n)^n * x^n/n!.
%H Vaclav Kotesovec, <a href="/A228563/b228563.txt">Table of n, a(n) for n = 0..100</a>
%F E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 109*x^4/4! + 1241*x^5/5! +...
%F where
%F A(x) = 1 + (1+x*A(x))*x + (1+x*A(x)^2)^2*x^2/2! + (1+x*A(x)^3)^3*x^3/3! + (1+x*A(x)^4)^4*x^4/4! + (1+x*A(x)^5)^5*x^5/5! +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0,n,(1+x*A^k +x*O(x^n))^k*x^k/k!));n!*polcoeff(A,n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A143768.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 25 2013
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