OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} (-3)^(n-k) * (Product_{j=0..k-1} (-3*j+1)) * Stirling2(n,k).
a(n) ~ n! * (-1)^(n+1) * Gamma(1/3) * 3^(n - 1/2) / (Pi * 2^(2/3) * n^(4/3) * log(2)^(n - 1/3)). - Vaclav Kotesovec, Mar 06 2022
MATHEMATICA
m = 17; Range[0, m]! * CoefficientList[Series[(2 - Exp[-3*x])^(1/3), {x, 0, m}], x] (* Amiram Eldar, Mar 05 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((2-exp(-3*x))^(1/3)))
(PARI) a(n) = sum(k=0, n, (-3)^(n-k)*prod(j=0, k-1, -3*j+1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 05 2022
STATUS
approved