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 A352985 #15 Apr 14 2022 02:38:14
%S A352985 1,0,1,1,2,5,18,74,339,1770,10915,79555,663140,6109351,61264436,
%T A352985 669862580,8044351557,106331744724,1536980041573,24028469781765,
%U A352985 402558463751974,7195932984364585,137204787854813174,2792969599543659326,60668198155262809815
%N A352985 a(n) = Sum_{k=0..floor(n/2)} k^(2*(n-2*k)).
%F A352985 G.f.: Sum_{k>=0} x^(2 * k) / (1 - k^2 * x).
%F A352985 a(n) ~ sqrt(Pi/2) * (n/(2*LambertW(exp(1)*n/2)))^(2*n + 1/2 - 2*n/LambertW(exp(1)*n/2)) / sqrt(1 + LambertW(exp(1)*n/2)). - _Vaclav Kotesovec_, Apr 14 2022
%t A352985 a[0] = 1; a[n_] := Sum[k^(2*(n - 2*k)), {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* _Amiram Eldar_, Apr 13 2022 *)
%o A352985 (PARI) a(n) = sum(k=0, n\2, k^(2*(n-2*k)));
%o A352985 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/(1-k^2*x)))
%Y A352985 Cf. A104872, A352983.
%K A352985 nonn,easy
%O A352985 0,5
%A A352985 _Seiichi Manyama_, Apr 13 2022