OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor((n-1)/2)} 4^(n-1-2*k) * Stirling2(n,2*k+1).
a(n) ~ 2^(2*n-1) * exp(n/LambertW(4*n) - n - 1/4) * n^n / (LambertW(4*n)^n * sqrt(1 + LambertW(4*n))). - Vaclav Kotesovec, Oct 07 2022
MATHEMATICA
With[{m = 20}, Range[0, m]! * CoefficientList[Series[Sinh[(Exp[4*x] - 1)/4], {x, 0, m}], x]] (* Amiram Eldar, Oct 07 2022 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(4*x)-1)/4))))
(PARI) a(n) = sum(k=0, (n-1)\2, 4^(n-1-2*k)*stirling(n, 2*k+1, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 07 2022
STATUS
approved