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 A360018 #26 Feb 20 2023 06:13:39
%S A360018 1,1,4,28,288,3854,63104,1220729,27248128,689446671,19501121536,
%T A360018 609753349945,20883798220800,777529328875208,31266494467227648,
%U A360018 1350520199148276667,62360172065142341632,3065369553470816704832,159818389764050045894656
%N A360018 Expansion of Sum_{k>=0} (k * x * (1 + (k * x)^2))^k.
%F A360018 a(n) = Sum_{k=0..floor(n/3)} (n-2*k)^n * binomial(n-2*k,k).
%F A360018 a(n) ~ c * (1-2*r)^(2*(1-r)*n) * n^n / ((1-3*r)^((1-3*r)*n) * r^(r*n)), where r = 0.06730326916452804898090832100482072129668759014637687455288... is the root of the equation (1-2*r) * log((1-3*r)^3 / (r*(1-2*r)^2)) = 2 and c = 0.77456580764856204420602709595934338976380573814558378938814706465915... - _Vaclav Kotesovec_, Feb 20 2023
%o A360018 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+(k*x)^2))^k))
%o A360018 (PARI) a(n) = sum(k=0, n\3, (n-2*k)^n*binomial(n-2*k, k));
%Y A360018 Cf. A360032, A360618.
%Y A360018 Cf. A360730.
%K A360018 nonn
%O A360018 0,3
%A A360018 _Seiichi Manyama_, Feb 19 2023