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 A320287 #10 Sep 08 2022 08:46:23
%S A320287 1,2,6,56,2050,318752,252035714,980755711616,23647746367946754,
%T A320287 3088949241542073508352,2940240000900000020000000002,
%U A320287 16218429504693724464229916894517248,748528620411995327278028288988088683724802,210422023062476527874650307058798916093350502080512
%N A320287 a(n) = n! * [x^n] Sum_{k>=0} exp(n^k*x)*x^k/k!.
%H A320287 G. C. Greubel, <a href="/A320287/b320287.txt">Table of n, a(n) for n = 0..48</a>
%F A320287 a(n) = [x^n] Sum_{k>=0} x^k/(1 - n^k*x)^(k+1).
%F A320287 a(n) = Sum_{k=0..n} binomial(n,k)*n^(k*(n-k)).
%F A320287 a(n) ~ 2^(n + 1/2) * n^(n^2/4 - 1/2) / sqrt(Pi) if n is even and a(n) ~ 2^(n + 3/2) * n^(n^2/4 - 3/4) / sqrt(Pi) if n is odd. - _Vaclav Kotesovec_, Jul 06 2022
%t A320287 Join[{1}, Table[n! SeriesCoefficient[Sum[Exp[n^k x] x^k/k!, {k, 0, n}], {x, 0, n}], {n, 13}]]
%t A320287 Join[{1}, Table[SeriesCoefficient[Sum[x^k/(1 - n^k x)^(k + 1), {k, 0, n}], {x, 0, n}], {n, 13}]]
%t A320287 Join[{1}, Table[Sum[Binomial[n, k] n^(k (n - k)), {k, 0, n}], {n, 13}]]
%o A320287 (PARI) for(n=0,20, print1(sum(k=0,n, binomial(n,k)*n^(k*(n-k))), ", ")) \\ _G. C. Greubel_, Nov 04 2018
%o A320287 (Magma) [(&+[Binomial(n,k)*n^(k*(n-k)):k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Nov 04 2018
%Y A320287 Cf. A047863, A135079.
%K A320287 nonn
%O A320287 0,2
%A A320287 _Ilya Gutkovskiy_, Oct 09 2018