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 A352944 #20 Dec 12 2022 16:56:34
%S A352944 1,1,1,2,3,5,9,16,31,61,125,266,579,1305,3009,7120,17255,42697,108005,
%T A352944 278466,731883,1958589,5331625,14758720,41501135,118507301,343405709,
%U A352944 1009313322,3007557523,9081204849,27775308049,86014412384,269603741111,855012176081
%N A352944 a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^k.
%F A352944 G.f.: Sum_{k>=0} x^k / (1 - k * x^2).
%F A352944 a(n) ~ sqrt(Pi) * (n/LambertW(exp(1)*n))^((n + 1 - n/LambertW(exp(1)*n))/2) / sqrt(1 + LambertW(exp(1)*n)). - _Vaclav Kotesovec_, Apr 14 2022
%t A352944 Join[{1},Table[Sum[(n-2k)^k,{k,0,Floor[n/2]}],{n,40}]] (* _Harvey P. Dale_, Dec 12 2022 *)
%o A352944 (PARI) a(n) = sum(k=0, n\2, (n-2*k)^k);
%o A352944 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^2)))
%Y A352944 Cf. A026898, A104872, A352946.
%Y A352944 Cf. A087811.
%K A352944 nonn,easy
%O A352944 0,4
%A A352944 _Seiichi Manyama_, Apr 09 2022