A290215 a(n) = n! * [x^n] -exp(-n*x)*LambertW(-x).

0, 1, -2, 18, -144, 1900, -26820, 485394, -9679936, 225394488, -5765768100, 164923889350, -5132384691984, 174433050454260, -6385752833589220, 251596880714336850, -10585338808667808000, 474507594337155230704, -22550580127644413987268

Offset: 0

Author

Ilya Gutkovskiy, Oct 06 2017

Keywords

• sign

Comments

The n-th term of the n-th inverse binomial transform of A000169 (with A000169(0) = 0).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000169, A277474, A292633.

Programs

Mathematica

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

Formula

a(n) ~ -(-1)^n * LambertW(1) * n^n. - Vaclav Kotesovec, Oct 06 2017