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%I #8 Aug 21 2018 04:41:47
%S 1,-1,0,-18,208,-2400,36504,-663754,13808320,-324176418,8487126400,
%T -245122390601,7741417124880,-265402847130421,9816338228638872,
%U -389618889514254225,16518399076342421248,-745025763154442071130,35619835529954597786208,-1799459812004380374518790,95780758238408017088795600
%N a(n) = [x^n] Product_{k>=1} 1/(1 + n*x^k)^k.
%F a(n) ~ (-1)^n * n^n * (1 - 2/n + 6/n^2 - 14/n^3 + 33/n^4 - 70/n^5 + 149/n^6 - 298/n^7 + 591/n^8 - 1132/n^9 + 2139/n^10 + ...), for coefficients, see A005380. - _Vaclav Kotesovec_, Aug 21 2018
%t Table[SeriesCoefficient[Product[1/(1 + n x^k)^k, {k, 1, n}], {x, 0, n}], {n, 0, 20}]
%Y Cf. A255528, A261566, A261567, A266971, A292134, A297326, A298985, A298986, A298987.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Jan 31 2018
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