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 A353016 #17 Apr 16 2022 11:34:31
%S A353016 1,1,1,2,5,11,33,108,357,1405,5713,24670,117413,574007,3004577,
%T A353016 16608120,95057925,576245913,3622049809,23693870554,161816447365,
%U A353016 1140392550275,8351286979745,63206781102116,493344133444389,3980464191557205,33029872125113937,282290255465835382
%N A353016 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*k).
%F A353016 G.f.: Sum_{k>=0} x^k / (1 - (k * x)^2).
%F A353016 a(n) = (A062811(n) + 1)/2 for n > 0. - _Hugo Pfoertner_, Apr 16 2022
%t A353016 a[0] = 1; a[n_] := Sum[(n-2*k)^(2*k), {k, 0, Floor[n/2]}]; Array[a, 30, 0] (* _Amiram Eldar_, Apr 16 2022 *)
%o A353016 (PARI) a(n) = sum(k=0, n\2, (n-2*k)^(2*k));
%o A353016 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k*x)^2)))
%Y A353016 Cf. A062811, A352082, A352944.
%K A353016 nonn,easy
%O A353016 0,4
%A A353016 _Seiichi Manyama_, Apr 16 2022