OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..361
FORMULA
a(n) = Sum_{k=0..n} (2*n-k+1)^(k-1) * Stirling2(n,k).
a(n) ~ s * n^(n-1) / (sqrt(2*(1 + 2*r*s^2) - 2/(1 + log(s))) * exp(n) * r^n), where r = 0.2229533052706631261980294005821031136702825459439... and s = 1.759796045489338472919926226485178994146849909897... are roots of the system of equations exp(r*s^2) = 1 + s*log(s), 2*exp(r*s^2)*r*s = 1 + log(s). - Vaclav Kotesovec, Nov 25 2021
MATHEMATICA
Table[Sum[(2*n - k + 1)^(k-1) * StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 25 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, (2*n-k+1)^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 22 2021
STATUS
approved