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