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%I #9 Oct 07 2020 08:15:37
%S 1,2,4,36,168,1440,13920,134400,1619520,20549760,294631680,4449096960,
%T 74429752320,1312794362880,24870628823040,501316411115520,
%U 10661299747338240,239672059847700480,5664762159214878720
%N E.g.f.: A(x) = Product_{n>=1} (1 + 2*x^n/n)^n.
%H Vaclav Kotesovec, <a href="/A182965/b182965.txt">Table of n, a(n) for n = 0..439</a>
%e E.g.f.: A(x) = 1 + 2*x + 4*x^2/2! + 36*x^3/3! + 168*x^4/4! +...
%e A(x) = (1+2x)*(1+2x^2/2)^2*(1+2x^3/3)^3*(1+2x^4/4)^4*(1+2x^5/5)^5*...
%t nmax = 20; CoefficientList[Series[Product[(1 + 2*x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 07 2020 *)
%o (PARI) {a(n,k=2)=n!*polcoeff(prod(m=1,n,(1+k*x^m/m+x*O(x^n))^m),n)}
%Y Cf. A181541, A182966, A182967, A007838.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Dec 19 2010
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