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%I #18 Jun 18 2018 19:07:21
%S 1,-1,-2,-4,-18,-84,-564,-3984,-33504,-307728,-3156192,-35254080,
%T -429350400,-5641133760,-79720588800,-1204747741440,-19400679325440,
%U -331599765565440,-5996988417784320,-114408970262922240,-2296442484579686400,-48379417944213196800
%N Expansion of Product_{k>=1} (1 - k!*x^k).
%H G. C. Greubel, <a href="/A292280/b292280.txt">Table of n, a(n) for n = 0..445</a>
%F Convolution inverse of A077365.
%F a(n) ~ -n! * (1 - 1/n - 2/n^2 - 6/n^3 - 32/n^4 - 222/n^5 - 1916/n^6 - 19650/n^7 - 231200/n^8 - 3058566/n^9 - 44883428/n^10). - _Vaclav Kotesovec_, Sep 14 2017
%F G.f.: exp(-Sum_{k>=1} Sum_{j>=1} (j!)^k*x^(j*k)/k). - _Ilya Gutkovskiy_, Jun 18 2018
%t nmax = 25; CoefficientList[Series[Product[(1 - k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 13 2017 *)
%o (PARI) {a(n) = polcoeff(prod(k=1, n, 1-k!*x^k+x*O(x^n)), n)}
%Y Cf. A077365, A265950.
%K sign
%O 0,3
%A _Seiichi Manyama_, Sep 13 2017
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