OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..350
FORMULA
a(n) = Sum_{k=0..n} 5^k * k! * |Stirling1(n,k)|.
a(0) = 1; a(n) = 5 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (5 * exp(4*n/5) * (exp(1/5) - 1)^(n+1)). - Vaclav Kotesovec, Nov 11 2023
MATHEMATICA
a[n_] := Sum[5^k * k! * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 13 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, 5^k*k!*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2023
STATUS
approved