OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..328
FORMULA
a(n) = Sum_{k=0..n} (3*n+1)^(k-1) * Stirling2(n,k).
a(n) ~ s * n^(n-1) / (3 * sqrt(1 + r*s^3) * exp(n) * r^n), where r = LambertW(1/3)/exp(1/LambertW(1/3) - 3) = 0.106691814639676411952403096776061... and s = exp(1/(3*LambertW(1/3)) - 1) = 1.341591995635184131204677967393502... are roots of the system of equations exp(r*s^3) = 1 + log(s), 3*r*s^3*exp(r*s^3) = 1. - Vaclav Kotesovec, Nov 26 2021
MATHEMATICA
nterms=20; Table[Sum[(3n+1)^(k-1)*StirlingS2[n, k], {k, 0, n}], {n, 0, nterms-1}] (* Paolo Xausa, Nov 25 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, (3*n+1)^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 25 2021
STATUS
approved