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 A353013 #15 Apr 16 2022 09:39:23
%S A353013 1,1,4,28,264,3207,47696,839412,17061280,393264145,10135913792,
%T A353013 288839201432,9017184333440,306045200463519,11220008681600256,
%U A353013 441866073895351128,18603606156815235584,833860238440653331505,39643749441387211150336
%N A353013 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(n-k).
%F A353013 G.f.: Sum_{k>=0} (k * x)^k / (1 - k * x^2).
%t A353013 a[0] = 1; a[n_] := Sum[(n - 2*k)^(n - k), {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* _Amiram Eldar_, Apr 16 2022 *)
%o A353013 (PARI) a(n) = sum(k=0, n\2, (n-2*k)^(n-k));
%o A353013 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k*x^2)))
%Y A353013 Cf. A031971, A353014.
%Y A353013 Cf. A352981, A352944.
%K A353013 nonn,easy
%O A353013 0,3
%A A353013 _Seiichi Manyama_, Apr 16 2022