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 A358688 #16 Nov 27 2022 06:44:34
%S A358688 1,2,5,34,869,75866,28213327,39049033346,256215628707257,
%T A358688 7710689746589777938,1063776147486867074877851,
%U A358688 870059224717752809087935599002,3104894940194751778363241199111802885,77521065749331962430758061530260243383954602
%N A358688 a(n) = n! * Sum_{k=0..n} k^(k * (n-k)) / (n-k)!.
%H A358688 Seiichi Manyama, <a href="/A358688/b358688.txt">Table of n, a(n) for n = 0..51</a>
%F A358688 E.g.f.: Sum_{k>=0} x^k * exp(k^k * x).
%F A358688 G.f.: Sum_{k>=0} k! * x^k / (1 - k^k * x)^(k+1).
%t A358688 Table[1 + n!*Sum[k^(k*(n-k))/(n-k)!, {k, 1, n}], {n, 0, 12}] (* _Vaclav Kotesovec_, Nov 27 2022 *)
%o A358688 (PARI) a(n) = n!*sum(k=0, n, k^(k*(n-k))/(n-k)!);
%o A358688 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k*exp(x)^k^k)))
%o A358688 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k/(1-k^k*x)^(k+1)))
%Y A358688 Cf. A006153, A193421, A358687.
%Y A358688 Cf. A349893, A356674.
%K A358688 nonn
%O A358688 0,2
%A A358688 _Seiichi Manyama_, Nov 26 2022