OFFSET
0,4
LINKS
FORMULA
a(n) = Sum_{k=1..n} Stirling1(n, k)*k^(k-1).
a(n) ~ (exp(exp(-1))-1)^(1/2-n) * exp(-exp(-1)/2+1/2-n) * n^(n-1).
E.g.f.: Series_Reversion( exp(x * exp(-x)) - 1 ). - Seiichi Manyama, Sep 10 2024
MATHEMATICA
CoefficientList[Series[-LambertW[-Log[1+x]], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[StirlingS1[n, k]*k^(k-1), {k, 1, n}], {n, 0, 20}]
PROG
(PARI) my(x='x+O('x^50)); concat([0], Vec(serlaplace(-lambertw(-log(1+x))))) \\ G. C. Greubel, Jun 21 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 17 2016
STATUS
approved