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A181541 E.g.f.: A(x) = Product_{n>=1} (1 + x^n/n)^n. 9

%I #14 Oct 07 2020 08:08:46

%S 1,1,2,12,54,390,3120,28140,290640,3354960,42561120,586259520,

%T 8806422240,141680579040,2446025662080,44990666360640,877867974023040,

%U 18115179826423680,394351821275892480,9019730566889602560

%N E.g.f.: A(x) = Product_{n>=1} (1 + x^n/n)^n.

%H Seiichi Manyama, <a href="/A181541/b181541.txt">Table of n, a(n) for n = 0..444</a>

%F E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*(-j)^(k-1))). - _Ilya Gutkovskiy_, Sep 12 2018

%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 12*x^3/3! + 54*x^4/4! + 390*x^5/5! + ...

%e A(x) = (1+x)*(1 + x^2/2)^2*(1 + x^3/3)^3*(1 + x^4/4)^4*(1 + x^5/5)^5*...

%t nmax = 20; CoefficientList[Series[Product[(1+x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 07 2020 *)

%o (PARI) {a(n)=n!*polcoeff(prod(m=1,n,(1+x^m/m+x*O(x^n))^m),n)}

%Y Cf. A007838, A294469.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 02 2010

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