OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
FORMULA
a(n) ~ arcsinh(exp(-1)) * n^(n-1).
a(n) ~ (-1 + log(1 + sqrt(1+exp(2)))) * n^(n-1).
MATHEMATICA
CoefficientList[Series[-ArcSinh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Flatten[{0, Table[Sum[Sin[Pi*k/2] * Binomial[n, k] * (k-2)!!^2 * (n-k)^(n-k-1), {k, 1, n-1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 28 2016 *)
PROG
(PARI) x='x+O('x^10); concat([0, 0], Vec(serlaplace(-asinh(x)*lambertw(-x) ))) \\ G. C. Greubel, Nov 08 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 17 2016
STATUS
approved