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%I #8 Oct 07 2020 08:15:50
%S 1,3,6,72,342,3330,36720,366660,4974480,67178160,1043189280,
%T 16836906240,303306806880,5705780240160,114832957599360,
%U 2475901844095680,55754442891987840,1331875774475326080,33292197644365820160
%N E.g.f.: A(x) = Product_{n>=1} (1 + 3*x^n/n)^n.
%H Vaclav Kotesovec, <a href="/A182966/b182966.txt">Table of n, a(n) for n = 0..438</a>
%e E.g.f.: A(x) = 1 + 3*x + 6*x^2/2! + 72*x^3/3! + 342*x^4/4! +...
%e A(x) = (1+3x)*(1+3x^2/2)^2*(1+3x^3/3)^3*(1+3x^4/4)^4*(1+3x^5/5)^5*...
%t nmax = 20; CoefficientList[Series[Product[(1 + 3*x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 07 2020 *)
%o (PARI) {a(n,k=3)=n!*polcoeff(prod(m=1,n,(1+k*x^m/m+x*O(x^n))^m),n)}
%Y Cf. A181541, A182965, A182967, A007838.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Dec 19 2010
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