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A351768
a(n) = n! * Sum_{k=0..n} k^(n-k) * (n-k)^k/k!.
3
1, 0, 2, 18, 276, 6260, 190950, 7523082, 371286440, 22356290952, 1608686057610, 136069954606190, 13345029902628732, 1500054487474871484, 191349476316804534638, 27464505325501082617170, 4402551348139824475260240, 783025812197886669354545552
OFFSET
0,3
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
MATHEMATICA
Join[{1}, Table[n!*Sum[k^(n-k) * (n-k)^k/k!, {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Feb 19 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, k^(n-k)*(n-k)^k/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 18 2022
STATUS
approved