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

0,3

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

Formula

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

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}]

Crossrefs

Cf. A000169, A277474, A292633.

Sequence in context: A001804 A277182 A052640 * A208654 A037565 A329170

Adjacent sequences: A290212 A290213 A290214 * A290216 A290217 A290218

Keyword

sign

Author

Ilya Gutkovskiy, Oct 06 2017

Status

approved