%I #29 Sep 08 2022 08:44:48
%S 1,1,5,32,304,3537,52010,895397,18016416,410889848,10523505770,
%T 298220329546,9274349837081,313761671751672,11474635626789410,
%U 450964042480390679,18954785687060988578,848386888530723146912
%N Expansion of g.f.: 1/Product_{n>0} (1 - n^n * x^n).
%H Vaclav Kotesovec, <a href="/A023882/b023882.txt">Table of n, a(n) for n = 0..380</a>
%F Log of g.f.: Sum_{k>=1} (sigma(k, k+1)/k) x^k, where sigma(k, q) is the sum of the q-th powers of the divisors of k.
%F a(n) ~ n^n * (1 + exp(-1)/n + (1/2*exp(-1)+5*exp(-2))/n^2). - _Vaclav Kotesovec_, Dec 19 2015
%F a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} A294645(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Nov 09 2017
%p seq(coeff(series(1/mul(1-k^k*x^k,k=1..n),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 31 2018
%t nmax=20; CoefficientList[Series[Product[1/(1-k^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Dec 19 2015 *)
%o (PARI) m=20; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-k^k*x^k))) \\ _G. C. Greubel_, Oct 30 2018
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-k^k*x^k): k in [1..m]]) )); // _G. C. Greubel_, Oct 30 2018
%Y Cf. A265949, A292312, A294645.
%K nonn
%O 0,3
%A _Olivier Gérard_