OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} (n+2*k)!/(n+k+1)! * Stirling1(n,k).
a(n) ~ s^2 * sqrt((2-s) / (-2*s^3 + 5*s^2 + 4*s - 4)) * n^(n-1) / (r^n * exp(n)), where r = 0.1660717422585514666099422406611296365893647754849... and s = 1.527702505127565301209742745041094767065375131037... are real roots of the system of equations 1 + s^2*log(1 + r*s) = s, 2/s - r*s^2/(1 + r*s) = 1. - Vaclav Kotesovec, Nov 07 2023
MATHEMATICA
Table[Sum[(n + 2*k)!/(n + k + 1)!*StirlingS1[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 07 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (n+2*k)!/(n+k+1)!*stirling(n, k, 1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 07 2023
STATUS
approved