A335867 a(n) = exp(-n) * Sum_{k>=0} n^k * (k - 1)^n / k!.

1, 0, 3, 29, 397, 6879, 144751, 3587100, 102351929, 3305310065, 119186370091, 4746969337923, 206966647324933, 9804683604806908, 501491905963040903, 27544070654283355889, 1616869985889305862385, 101020181695996141703335, 6693303018177050431484035, 468770856837303230888704208

Offset: 0

Author

Ilya Gutkovskiy, Jun 27 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A000296, A217924, A242817, A334240, A335868.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[n (Exp[x] - 1) - x], {x, 0, n}], {n, 0, 19}]
Table[Sum[(-1)^(n - k) Binomial[n, k] BellB[k, n], {k, 0, n}], {n, 0, 19}]

Formula

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

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