OFFSET
0,3
FORMULA
a(n) = n! * [x^n] exp(-x) / (2 - exp(n*x)).
a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * n^k * A000670(k).
a(n) ~ n^n * n! / (2 * (log(2))^(n+1)). - Vaclav Kotesovec, Dec 19 2019
MATHEMATICA
Table[Sum[(n k - 1)^n/2^(k + 1), {k, 0, Infinity}], {n, 0, 15}]
Join[{1}, Table[n^n HurwitzLerchPhi[1/2, -n, -1/n]/2, {n, 1, 15}]]
Table[n! SeriesCoefficient[Exp[-x]/(2 - Exp[n x]), {x, 0, n}], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 19 2019
STATUS
approved