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 A387483 #13 Sep 01 2025 06:55:12
%S A387483 1,0,2,4,4,32,24,144,304,576,2336,3648,13120,30208,70528,218368,
%T A387483 456448,1360896,3316224,8311808,23127040,54812672,151197696,380669952,
%U A387483 978595840,2613067776,6540566528,17464705024,44764708864,116183662592,305637064704,783627386880
%N A387483 a(n) = Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(k,n-2*k)^2.
%H A387483 Vincenzo Librandi, <a href="/A387483/b387483.txt">Table of n, a(n) for n = 0..2000</a>
%F A387483 G.f.: 1/sqrt((1-2*x^2-4*x^3)^2 - 32*x^5).
%t A387483 Table[Sum[2^(n-k)*Binomial[k,n-2*k]^2,{k,0,Floor[n/2]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387483 (PARI) a(n) = sum(k=0, n\2, 2^(n-k)*binomial(k, n-2*k)^2);
%o A387483 (Magma) [(&+[2^(n-k)* Binomial(k,n-2*k)^2: k in [0..Floor(n/2)]]): n in [0..40]]; // _Vincenzo Librandi_, Sep 01 2025
%Y A387483 Cf. A298567.
%K A387483 nonn,new
%O A387483 0,3
%A A387483 _Seiichi Manyama_, Aug 30 2025