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 A387554 #19 Sep 02 2025 11:48:15
%S A387554 1,0,2,4,3,20,16,56,117,152,510,700,1671,3532,5772,14480,24761,52400,
%T A387554 109114,198324,437899,821828,1670536,3423784,6547325,13666184,
%U A387554 26654966,53492716,108440335,212433276,432672004,857090304,1713987777,3452225824,6839636530
%N A387554 a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k+2,2*n-4*k+1).
%H A387554 Vincenzo Librandi, <a href="/A387554/b387554.txt">Table of n, a(n) for n = 0..1500</a>
%H A387554 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,4,-1,4,-4).
%F A387554 G.f.: B(x)^2, where B(x) is the g.f. of A387515.
%F A387554 G.f.: 1/((1-x^2-2*x^3)^2 - 8*x^5).
%F A387554 a(n) = 2*a(n-2) + 4*a(n-3) - a(n-4) + 4*a(n-5) - 4*a(n-6).
%t A387554 Table[Sum[2^(n-2*k)*Binomial[2*k+2, 2*n-4*k+1]/2,{k,0,Floor[n/2]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 02 2025 *)
%o A387554 (PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(2*k+2, 2*n-4*k+1))/2;
%o A387554 (Magma) [&+[2^(n-2*k) * Binomial(2*k+2, 2*n-4*k+1)/2: k in [0..Floor(n/2)]]: n in [0..40]]; // _Vincenzo Librandi_, Sep 02 2025
%Y A387554 Cf. A123957, A387515.
%K A387554 nonn,easy,new
%O A387554 0,3
%A A387554 _Seiichi Manyama_, Sep 02 2025