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 A387550 #15 Sep 02 2025 16:47:43
%S A387550 1,4,16,72,316,1376,6016,26304,114960,502464,2196224,9599360,41957312,
%T A387550 183389184,801566720,3503527936,15313395968,66932560896,292552200192,
%U A387550 1278701856768,5589014330368,24428744679424,106774384771072,466694846300160,2039853285314560
%N A387550 a(n) = (1/2) * Sum_{k=0..n} 2^k * binomial(2*k+2,2*n-2*k+1).
%H A387550 Vincenzo Librandi, <a href="/A387550/b387550.txt">Table of n, a(n) for n = 0..1000</a>
%H A387550 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,8,-4).
%F A387550 G.f.: B(x)^2, where B(x) is the g.f. of A375276.
%F A387550 G.f.: 1/((1-2*x-2*x^2)^2 - 16*x^3).
%F A387550 a(n) = 4*a(n-1) + 8*a(n-3) - 4*a(n-4).
%t A387550 Table[Sum[2^k*Binomial[2*k+2,2*n-2*k+1]/2,{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Sep 02 2025 *)
%o A387550 (PARI) a(n) = sum(k=0, n, 2^k*binomial(2*k+2, 2*n-2*k+1))/2;
%o A387550 (Magma) [&+[2^k * Binomial(2*k+2, 2*n-2*k+1)/2: k in [0..n]]: n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2025
%Y A387550 Cf. A375276.
%K A387550 nonn,easy,new
%O A387550 0,2
%A A387550 _Seiichi Manyama_, Sep 01 2025