A330149 Expansion of e.g.f. exp(-x) / (1 + log(1 - x)).

1, 0, 2, 7, 47, 368, 3494, 38673, 489341, 6966344, 110199090, 1917589771, 36402276107, 748629861016, 16580304397942, 393443385034069, 9958671117295737, 267824225078212336, 7626444798009902530, 229232204568273395919, 7252798333599466521575, 240948882537990850397536

Offset

0,3

Comments

Inverse binomial transform of A007840.

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * A007840(k).

a(n) ~ n! * exp(n + exp(-1) - 1) / (exp(1) - 1)^(n+1). - Vaclav Kotesovec, Dec 15 2019

a(n) = (-1)^n + Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Dec 19 2023

Mathematica

nmax = 21; CoefficientList[Series[Exp[-x]/(1 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A052841, A330150.

Cf. A007840, A291979.

Sequence in context: A276649 A091117 A056854 * A117141 A349965 A305533

Adjacent sequences: A330146 A330147 A330148 * A330150 A330151 A330152

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 03 2019

Status

approved