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 A360592 #28 Feb 17 2023 03:29:38
%S A360592 1,1,2,5,14,44,149,543,2096,8539,36444,162380,752181,3612037,17933038,
%T A360592 91843329,484280386,2624400428,14595111277,83178971707,485218783724,
%U A360592 2893881790823,17628815344600,109585578277012,694575012732989,4485139961090153,29486515600393930
%N A360592 G.f.: Sum_{k>=0} (1 + k*x)^k * x^k.
%H A360592 Vaclav Kotesovec, <a href="/A360592/b360592.txt">Table of n, a(n) for n = 0..760</a>
%F A360592 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k) * (n-k)^k.
%F A360592 a(n) ~ exp(exp(1/2)*sqrt(n/2) - 3*exp(1)/8) * n^(n/2) / 2^(n/2 + 1) * (1 + ((exp(1/2) + exp(-1/2))/2^(5/2) + 11*exp(3/2)/2^(9/2))/sqrt(n)).
%p A360592 N:= 40:
%p A360592 S:= series(add((1+k*x)^k*x^k, k=0..N),x,N+1):
%p A360592 seq(coeff(S,x,k),k=0..N); # _Robert Israel_, Feb 13 2023
%t A360592 nmax = 30; CoefficientList[Series[Sum[(1 + k*x)^k * x^k, {k, 0, nmax}], {x, 0, nmax}], x]
%t A360592 Flatten[{1, Table[Sum[Binomial[n-k, k] * (n-k)^k, {k, 0, n/2}], {n, 1, 30}]}]
%o A360592 (PARI) {a(n) = polcoeff(sum(m=0, n, (1 + m*x)^m * x^m + x*O(x^n)), n)};
%o A360592 for(n=0, 30, print1(a(n), ", "))
%Y A360592 Cf. A360232, A092366, A187018, A360699, A360707.
%K A360592 nonn
%O A360592 0,3
%A A360592 _Vaclav Kotesovec_, Feb 13 2023