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 A360699 #13 Feb 20 2023 03:16:36
%S A360699 1,0,1,1,1,4,5,9,28,43,97,281,507,1286,3666,7494,20470,58725,132484,
%T A360699 381700,1113180,2719887,8171219,24337511,63524916,197606643,602261524,
%U A360699 1662206380,5328738685,16628469912,48148703533,158544768073,506473892417,1529218062752,5159071807165
%N A360699 G.f.: Sum_{k>=0} (1 + k*x)^k * x^(2*k).
%H A360699 Vaclav Kotesovec, <a href="/A360699/b360699.txt">Table of n, a(n) for n = 0..1000</a>
%F A360699 a(n) = Sum_{k=0..n} binomial(k,n-2*k) * k^(n-2*k).
%F A360699 log(a(n)) ~ n/3 * log(n/3).
%F A360699 a(n) ~ exp(exp(1/3)*n^(1/3)/3^(1/3)) * n^(n/3) / 3^(n/3 + 1) * (1 + (3^(1/3)/(8*exp(1/3)) - 4*exp(2/3)/3^(5/3)) / n^(1/3) + (67/(128*3^(1/3)*exp(2/3)) + 8*exp(4/3)/3^(10/3)) / n^(2/3)).
%t A360699 nmax = 40; CoefficientList[Series[Sum[(1 + k*x)^k * x^(2*k), {k, 0, nmax}], {x, 0, nmax}], x]
%t A360699 Join[{1}, Table[Sum[Binomial[k, n - 2*k] * k^(n - 2*k), {k, 0, n}], {n, 1, 40}]]
%Y A360699 Cf. A360592, A360707, A360479.
%K A360699 nonn
%O A360699 0,6
%A A360699 _Vaclav Kotesovec_, Feb 16 2023