OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..344
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k) * (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(3 + 1/LambertW(-1/3)) = 0.15501985846382288988548853891763630846... and s = exp(1 + 1/(3*LambertW(-1/3))) = 1.5865317583949486858973892879410781361... are roots of the system of equations exp(-r*s^3) + log(s) = 1, exp(r*s^3) = 3*r*s^3. - Vaclav Kotesovec, Nov 26 2021
MATHEMATICA
nterms=20; Table[Sum[(-1)^(n-k)(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, (-1)^(n-k)*(3*n+1)^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 25 2021
STATUS
approved