A335868 a(n) = exp(n) * Sum_{k>=0} (-n)^k * (k - 1)^n / k!.

1, -2, 7, -31, 149, -631, 475, 43210, -844727, 10960505, -86569889, -584746911, 46302579229, -1304510879686, 25366896568707, -277053418780891, -4271166460501743, 384590020131637825, -14617527176248527545, 380117694164438489422, -5265650620303861935579

Offset: 0

Author

Ilya Gutkovskiy, Jun 27 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..200
• Eric Weisstein's World of Mathematics, Bell Polynomial

Crossrefs

Cf. A109747, A292866, A334241, A335867.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[n (1 - Exp[x]) - x], {x, 0, n}], {n, 0, 20}]
Table[Sum[(-1)^(n - k) Binomial[n, k] BellB[k, -n], {k, 0, n}], {n, 0, 20}]

Formula

a(n) = n! * [x^n] exp(n*(1 - exp(x)) - x).

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