A302398 a(n) = n! * [x^n] 1/(1 + x*exp(n*x)).

1, -1, -2, 3, 248, 5655, 62064, -3516625, -376936064, -21890186577, -495165203200, 96687112380639, 20607024735783936, 2471270260977141767, 142697263160045590528, -25986252776953159328625, -11860424645318274482077696, -2719428501410438623907546529, -372732332273232481973818294272

Offset: 0

Author

Ilya Gutkovskiy, Apr 07 2018

Keywords

• sign

Crossrefs

Cf. A134095, A235328, A302397.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(1 + x Exp[n x]), {x, 0, n}], {n, 0, 18}]
Join[{1}, Table[n! Sum[(-1)^(n - k) (n (n - k))^k/k!, {k, 0, n}], {n, 18}]]
Join[{1}, Table[Sum[(-1)^k k! (n k)^(n - k) Binomial[n, k], {k, 0, n}], {n, 18}]]

Formula

a(n) = n!*Sum_{k=0..n} (-1)^(n-k)*(n*(n-k))^k/k!.

a(n) = Sum_{k=0..n} (-1)^k*k!*(n*k)^(n-k)*binomial(n,k).