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A330149
Expansion of e.g.f. exp(-x) / (1 + log(1 - x)).
7
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.
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 03 2019
STATUS
approved