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 A387515 #16 Sep 01 2025 16:59:42
%S A387515 1,0,1,2,1,8,5,18,37,40,145,178,417,872,1301,3330,5365,11080,22801,
%T A387515 39362,86721,157128,312293,631666,1169541,2416104,4602961,9061458,
%U A387515 18123553,34717608,69825013,135902818,267384405,531611656,1035512785,2060791650,4048647489,7979180296
%N A387515 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(k,n-2*k)^2.
%H A387515 Vincenzo Librandi, <a href="/A387515/b387515.txt">Table of n, a(n) for n = 0..2000</a>
%F A387515 G.f.: 1/sqrt((1-x^2-2*x^3)^2 - 8*x^5).
%t A387515 Table[Sum[2^(n-2*k)*Binomial[k,n-2*k]^2,{k,0,Floor[n/2]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387515 (PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(k, n-2*k)^2);
%o A387515 (Magma) [(&+[2^(n-2*k) * Binomial(k,n-2*k)^2: k in [0..Floor(n/2)]]): n in [0..40]]; // _Vincenzo Librandi_, Sep 01 2025
%Y A387515 Cf. A108488, A387516.
%Y A387515 Cf. A387481, A387483.
%K A387515 nonn,new
%O A387515 0,4
%A A387515 _Seiichi Manyama_, Sep 01 2025