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%I #4 Apr 07 2018 10:11:10
%S 1,-1,-2,3,248,5655,62064,-3516625,-376936064,-21890186577,
%T -495165203200,96687112380639,20607024735783936,2471270260977141767,
%U 142697263160045590528,-25986252776953159328625,-11860424645318274482077696,-2719428501410438623907546529,-372732332273232481973818294272
%N a(n) = n! * [x^n] 1/(1 + x*exp(n*x)).
%F a(n) = n!*Sum_{k=0..n} (-1)^(n-k)*(n*(n-k))^k/k!.
%F a(n) = Sum_{k=0..n} (-1)^k*k!*(n*k)^(n-k)*binomial(n,k).
%t Table[n! SeriesCoefficient[1/(1 + x Exp[n x]), {x, 0, n}], {n, 0, 18}]
%t Join[{1}, Table[n! Sum[(-1)^(n - k) (n (n - k))^k/k!, {k, 0, n}], {n, 18}]]
%t Join[{1}, Table[Sum[(-1)^k k! (n k)^(n - k) Binomial[n, k], {k, 0, n}], {n, 18}]]
%Y Cf. A134095, A235328, A302397.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Apr 07 2018
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