%I #20 Jun 18 2018 18:51:47
%S 1,-1,-1,-5,-15,-93,-551,-4129,-33607,-312929,-3179343,-35602881,
%T -432201743,-5678740945,-80142780751,-1210609725905,-19481112885231,
%U -332836223507793,-6016678424942063,-114746996449871761,-2302527084416470255,-48495552665272893329
%N Expansion of 1/Product_{k>=1} (1 + k!*x^k).
%H G. C. Greubel, <a href="/A292279/b292279.txt">Table of n, a(n) for n = 0..445</a>
%F Convolution inverse of A265950.
%F a(n) ~ -n! * (1 - 1/n - 1/n^2 - 6/n^3 - 31/n^4 - 219/n^5 - 1932/n^6 - 19945/n^7 - 234837/n^8 - 3104108/n^9 - 45495817/n^10). - _Vaclav Kotesovec_, Sep 14 2017
%F G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*(j!)^k*x^(j*k)/k). - _Ilya Gutkovskiy_, Jun 18 2018
%t nmax = 25; CoefficientList[Series[Product[1/(1 + k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 13 2017 *)
%o (PARI) {a(n) = polcoeff(1/prod(k=1, n, 1+k!*x^k+x*O(x^n)), n)}
%Y Cf. A077365, A265950.
%K sign
%O 0,4
%A _Seiichi Manyama_, Sep 13 2017