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 A387551 #17 Sep 02 2025 15:46:25
%S A387551 1,0,4,4,12,40,44,224,304,992,2208,4480,13200,24320,68608,145856,
%T A387551 345920,848256,1834432,4644864,10239488,24708096,57602048,132493312,
%U A387551 318103808,724885504,1728687104,4003968000,9371413504,22045935616,51113446400,120583479296
%N A387551 a(n) = (1/2) * Sum_{k=0..floor(n/2)} 2^k * binomial(2*k+2,2*n-4*k+1).
%H A387551 Vincenzo Librandi, <a href="/A387551/b387551.txt">Table of n, a(n) for n = 0..1500</a>
%H A387551 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,4,-4,8,-4).
%F A387551 G.f.: B(x)^2, where B(x) is the g.f. of A387476.
%F A387551 G.f.: 1/((1-2*x^2-2*x^3)^2 - 16*x^5).
%F A387551 a(n) = 4*a(n-2) + 4*a(n-3) - 4*a(n-4) + 8*a(n-5) - 4*a(n-6).
%t A387551 Table[Sum[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 A387551 (PARI) a(n) = sum(k=0, n\2, 2^k*binomial(2*k+2, 2*n-4*k+1))/2;
%o A387551 (Magma) [&+[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 A387551 Cf. A387476.
%K A387551 nonn,easy,new
%O A387551 0,3
%A A387551 _Seiichi Manyama_, Sep 01 2025