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%I #9 Jul 23 2014 01:55:06
%S 1,1,3,19,215,4016,119092,5503205,393154477,43298176708,7340865004766,
%T 1913028475033699,764596866776205619,467416620805272150858,
%U 435773832975324764799712,617753035395626539657324801,1327738980050724547857227605753,4314831625390935798178255342966024
%N E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * Product_{k=1..n} A(k*x).
%H Vaclav Kotesovec, <a href="/A230317/b230317.txt">Table of n, a(n) for n = 0..76</a>
%e G.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 215*x^4/4! + 4016*x^5/5! +...
%e where
%e A(x) = 1 + x*A(x) + x^2*A(x)*A(2*x)/2! + x^3*A(x)*A(2*x)*A(3*x)/3! + x^4*A(x)*A(2*x)*A(3*x)*A(4*x)/4! + x^5*A(x)*A(2*x)*A(3*x)*A(4*x)*A(5*x)/5! +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m/m!*prod(k=1, m, subst(A, x, k*x+x*O(x^n))))); n!*polcoeff(A, n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A230321, A178087.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 15 2013
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