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 A351795 #18 Feb 21 2022 03:50:08
%S A351795 1,1,4,30,396,8360,256470,10619952,564959528,37370475648,
%T A351795 3001942868490,287388158562560,32278318416029532,4197544986996581376,
%U A351795 625014083479647028622,105554855135062180485120,20053957030647088382195280,4255329207190209023134564352
%N A351795 a(n) = n! * Sum_{k=0..n} (k * (n-k))^k/k!.
%H A351795 Vaclav Kotesovec, <a href="/A351795/b351795.txt">Table of n, a(n) for n = 0..266</a>
%H A351795 Vaclav Kotesovec, <a href="/A351795/a351795.jpg">Graph - the asymptotic ratio (10000 terms)</a>
%F A351795 a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / (sqrt(LambertW(exp(2)*n)^2 - 1) * exp(n*(1 - 1/LambertW(exp(2)*n))) * LambertW(exp(2)*n)^n). - _Vaclav Kotesovec_, Feb 20 2022
%t A351795 a[n_] := n!*(1 + Sum[(k*(n - k))^k/k!, {k, 1, n}]); Array[a, 18, 0] (* _Amiram Eldar_, Feb 19 2022 *)
%o A351795 (PARI) a(n) = n!*sum(k=0, n, (k*(n-k))^k/k!);
%Y A351795 Cf. A235328, A349965, A351768, A351796.
%K A351795 nonn
%O A351795 0,3
%A A351795 _Seiichi Manyama_, Feb 19 2022