OFFSET
0,2
FORMULA
a(0) = 1; a(n) = 2*n*a(n-1) + Sum_{k=1..n} (-1)^(k-1) * binomial(n,k) * a(n-k).
a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k+1)^k / k!.
a(n) ~ n! / (2 * LambertW(1/2)^(n+1) * (LambertW(1/2) + 1)). - Vaclav Kotesovec, Dec 29 2023
PROG
(PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k+1)^k/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 18 2023
STATUS
approved