A302581 a(n) = n! * [x^n] -exp(-n*x)*log(1 - x).

0, 1, -3, 20, -186, 2249, -33360, 586172, -11901008, 274098393, -7060189120, 201092672604, -6275340884736, 212915635727313, -7803567334571008, 307245946117223700, -12933084380738398208, 579587518114690731601, -27550568677612746940416, 1384553892443352890245636

Offset: 0

Author

Ilya Gutkovskiy, Apr 10 2018

Keywords

• sign

Links

• N. J. A. Sloane, Transforms
• Index entries for sequences related to logarithmic numbers

Crossrefs

Cf. A002104, A002741, A104150, A134095, A190314.

Programs

Mathematica

Table[n! SeriesCoefficient[-Exp[-n x] Log[1 - x], {x, 0, n}], {n, 0, 19}]
Table[Sum[(-n)^(n - k) (k - 1)! Binomial[n, k], {k, 1, n}], {n, 0, 19}]
nmax = 20; CoefficientList[Series[-Log[1 - LambertW[x]]/(1 + LambertW[x]), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 09 2019 *)

Formula

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

E.g.f.: -log(1 - LambertW(x))/(1 + LambertW(x)). - Vaclav Kotesovec, Jun 09 2019

a(n) ~ -(-1)^n * log(2) * n^n. - Vaclav Kotesovec, Jun 09 2019