A351768 a(n) = n! * Sum_{k=0..n} k^(n-k) * (n-k)^k/k!.

1, 0, 2, 18, 276, 6260, 190950, 7523082, 371286440, 22356290952, 1608686057610, 136069954606190, 13345029902628732, 1500054487474871484, 191349476316804534638, 27464505325501082617170, 4402551348139824475260240, 783025812197886669354545552

Offset: 0

Author

Seiichi Manyama, Feb 18 2022

Keywords

• nonn

Crossrefs

Cf. A006153, A062817, A134095, A351765, A351780.

Programs

Mathematica

Join[{1}, Table[n!*Sum[k^(n-k) * (n-k)^k/k!, {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Feb 19 2022 *)

PARI

a(n) = n!*sum(k=0, n, k^(n-k)*(n-k)^k/k!);

Formula

log(a(n)) ~ n *(2*log(n) - log(log(n)) - 2 + (log(log(n)) + log(log(n)-1) + 1)/log(n)). - Vaclav Kotesovec, Feb 19 2022