A334243 a(n) = exp(n) * Sum_{k>=0} (k + n)^n * (-n)^k / k!.

1, 0, -2, -3, 44, 245, -2346, -33278, 186808, 6888555, -6774910, -1986368439, -10227075420, 738830661296, 10363304656782, -327255834908715, -9380517430358288, 152180429032236325, 9132761207739810618, -46897839494116200918, -9833058047657527541220

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Eric Weisstein's World of Mathematics, Bell Polynomial

Formula

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

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

Mathematica

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

Crossrefs

Cf. A292866, A298373, A334240, A334241, A334242.

Sequence in context: A354613 A355842 A100443 * A323619 A349559 A349827

Adjacent sequences: A334240 A334241 A334242 * A334244 A334245 A334246

Keyword

sign

Author

Ilya Gutkovskiy, Apr 19 2020

Status

approved