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 A356674 #15 Nov 27 2022 05:12:41
%S A356674 1,2,5,25,349,19941,4440391,4382699203,17687865017481,
%T A356674 356274213630958297,33338407933090938442411,
%U A356674 16214021627369697901867402911,43817834057167927861655409052462093,595284492835035398061242850538179192931525
%N A356674 a(n) = n! * Sum_{k=0..n} k^(k*(n-k))/k!.
%H A356674 Seiichi Manyama, <a href="/A356674/b356674.txt">Table of n, a(n) for n = 0..51</a>
%F A356674 E.g.f: Sum_{k>=0} x^k / (k! * (1 - k^k * x)).
%F A356674 log(a(n)) ~ n^2*log(n)/4 * (1 - log(2)/log(n) + 1/(4*log(n)^2)). - _Vaclav Kotesovec_, Nov 27 2022
%t A356674 Table[n!*(1 + Sum[k^(k*(n-k))/k!, {k, 1, n}]), {n, 0, 12}] (* _Vaclav Kotesovec_, Nov 27 2022 *)
%o A356674 (PARI) a(n) = n!*sum(k=0, n, k^(k*(n-k))/k!);
%o A356674 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k^k*x)))))
%Y A356674 Cf. A354436, A356672, A356673.
%Y A356674 Cf. A327578, A349893.
%K A356674 nonn
%O A356674 0,2
%A A356674 _Seiichi Manyama_, Aug 22 2022