OFFSET
0,3
FORMULA
E.g.f.: 1 / (1 - Sum_{k>=1} k^k*x^k/k!).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k^k * a(n-k).
a(n) ~ sqrt(Pi) * 2^(n - 3/2) * n^(n + 1/2) / exp(n/2). - Vaclav Kotesovec, Jun 29 2019
MATHEMATICA
nmax = 18; CoefficientList[Series[(1 + LambertW[-x])/(1 + 2 LambertW[-x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 29 2019
STATUS
approved