This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351768 #13 Feb 19 2022 04:25:27
%S A351768 1,0,2,18,276,6260,190950,7523082,371286440,22356290952,1608686057610,
%T A351768 136069954606190,13345029902628732,1500054487474871484,
%U A351768 191349476316804534638,27464505325501082617170,4402551348139824475260240,783025812197886669354545552
%N A351768 a(n) = n! * Sum_{k=0..n} k^(n-k) * (n-k)^k/k!.
%F A351768 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
%t A351768 Join[{1}, Table[n!*Sum[k^(n-k) * (n-k)^k/k!, {k, 0, n}], {n, 1, 20}]] (* _Vaclav Kotesovec_, Feb 19 2022 *)
%o A351768 (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*(n-k)^k/k!);
%Y A351768 Cf. A006153, A062817, A134095, A351765, A351780.
%K A351768 nonn
%O A351768 0,3
%A A351768 _Seiichi Manyama_, Feb 18 2022