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 A360618 #16 Feb 15 2023 14:02:19
%S A360618 1,1,5,43,515,7950,150086,3349945,86296849,2519907605,82249222661,
%T A360618 2967449372028,117266100841668,5037282382077353,233701540415817409,
%U A360618 11645959855678136519,620389246928233860127,35181554115178393462386,2116059351692554708911298
%N A360618 Expansion of Sum_{k>=0} (k * x * (1 + k*x))^k.
%H A360618 Seiichi Manyama, <a href="/A360618/b360618.txt">Table of n, a(n) for n = 0..373</a>
%F A360618 a(n) = Sum_{k=0..floor(n/2)} (n-k)^n * binomial(n-k,k).
%F A360618 a(n) ~ c * d^n * n^n, where d = (1-r)^(2-r) / (r^r * (1-2*r)^(1-2*r)) where r = 0.163662210494891118101893756356803907477984542... is the root of the equation (1-2*r)^2 = r*(1-r) * exp(1/(1-r)) and c = 0.78619174295244329885973980954744130517052330684023764340463604028671858569... - _Vaclav Kotesovec_, Feb 14 2023
%t A360618 Flatten[{1, Table[Sum[Binomial[n-k, k] * (n-k)^n, {k, 0, n/2}], {n, 1, 20}]}] (* _Vaclav Kotesovec_, Feb 14 2023 *)
%o A360618 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+k*x))^k))
%o A360618 (PARI) a(n) = sum(k=0, n\2, (n-k)^n*binomial(n-k, k));
%Y A360618 Cf. A072034, A360592, A360611.
%K A360618 nonn
%O A360618 0,3
%A A360618 _Seiichi Manyama_, Feb 14 2023