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 A298988 a(n) = [x^n] Product_{k>=1} 1/(1 + n*x^k)^k. 4

%I

%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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Last modified December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)