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 A387478 #13 Sep 01 2025 03:07:41
%S A387478 1,0,2,6,4,48,44,216,664,984,5216,9312,30160,93312,194528,717792,
%T A387478 1674688,4842624,14554304,35517312,112151680,293213568,823387136,
%U A387478 2409934848,6348908800,18760218624,51418362368,143838905856,414017065984,1132211048448,3255687793664
%N A387478 a(n) = Sum_{k=0..floor(n/2)} 2^k * 3^(n-2*k) * binomial(k,n-2*k)^2.
%H A387478 Vincenzo Librandi, <a href="/A387478/b387478.txt">Table of n, a(n) for n = 0..1000</a>
%F A387478 G.f.: 1/sqrt((1-2*x^2-6*x^3)^2 - 48*x^5).
%t A387478 Table[Sum[2^k* 3^(n-2*k)*Binomial[k,n-2*k]^2,{k,0,Floor[n/2]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 01 2025 *)
%o A387478 (PARI) a(n) = sum(k=0, n\2, 2^k*3^(n-2*k)*binomial(k, n-2*k)^2);
%o A387478 (Magma) [(&+[2^k *3^(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 A387478 Cf. A108490, A387479.
%K A387478 nonn,new
%O A387478 0,3
%A A387478 _Seiichi Manyama_, Aug 30 2025