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 A336213 #17 Jul 13 2020 08:26:07
%S A336213 1,2,9,163,12609,3906251,4835455813,23882051929709,470073929716006913,
%T A336213 36867039626275056203923,11562789460238169439667262501,
%U A336213 14393917436542502296957220221339601,72060131612303615870363237649174605005057,1424448870088911493303605765206905153730451241313
%N A336213 a(n) = Sum_{k=0..n} k^k * binomial(n,k)^n, with a(0)=1.
%H A336213 Seiichi Manyama, <a href="/A336213/b336213.txt">Table of n, a(n) for n = 0..58</a>
%H A336213 Vaclav Kotesovec, <a href="/A336213/a336213.jpg">Plot of a(n)/f(n) for n = 1..10000000</a>
%F A336213 Let f(n) = exp(-1/4) * QPochhammer(exp(-4)) * 2^(n^2 - 1/4) * exp((3*log(n)^2 + 3*log(2)^2 + Pi^2 - 1)/24) * n^((1 - log(2))/4) / Pi^(n/2). For sufficiently large n 0.985... < a(n)/f(n) < 1.015...
%F A336213 a(n) ~ exp(-1/4) * QPochhammer(exp(-4)) * QPochhammer(-n*exp(-1)/2, exp(-4)) * 2^(n^2) / Pi^(n/2) if n is even and a(n) ~ exp(-1/4) * QPochhammer(exp(-4)) * QPochhammer(-n*exp(-3)/2, exp(-4)) * sqrt(n) * 2^(n^2 - 1/2) / Pi^(n/2) if n is odd.
%t A336213 Table[1 + Sum[k^k * Binomial[n, k]^n, {k, 1, n}], {n, 0, 15}]
%o A336213 (PARI) a(n) = if (n==0, 1, sum(k=0, n, k^k * binomial(n,k)^n)); \\ _Michel Marcus_, Jul 13 2020
%Y A336213 Cf. A072034, A086331, A167008, A167010, A336188, A336204, A336212, A336214.
%K A336213 nonn
%O A336213 0,2
%A A336213 _Vaclav Kotesovec_, Jul 12 2020