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 A383573 #23 May 03 2025 22:26:07
%S A383573 1,2,7,24,89,338,1311,5152,20449,81778,328999,1330008,5398265,
%T A383573 21984610,89791103,367643776,1508560257,6201927074,25540266503,
%U A383573 105336838616,435035342553,1798875915826,7446653956895,30857577536800,127987031688161,531301328367762,2207281722474919
%N A383573 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k) * binomial(2*(n-2*k),n-2*k).
%H A383573 Vincenzo Librandi, <a href="/A383573/b383573.txt">Table of n, a(n) for n = 0..400</a>
%F A383573 G.f.: 1/sqrt((1 - x^2) * (1 - x^2 - 4*x)).
%F A383573 a(n) ~ phi^(3*n + 3) / (2^(3/2) * 5^(1/4) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, May 01 2025
%t A383573 Table[Sum[Binomial[n-k,k]* Binomial[2*(n-2*k),n-2*k],{k,0,Floor[n/2]}],{n,0,30}] (* _Vincenzo Librandi_, May 03 2025 *)
%o A383573 (PARI) a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(2*(n-2*k), n-2*k));
%o A383573 (Magma) [&+[Binomial(n-k, k) * Binomial(2*(n-2*k), n-2*k): k in [0..Floor(n div 2)]]: n in [0..35]]; // _Vincenzo Librandi_, May 03 2025
%Y A383573 Cf. A026375, A383581, A383582.
%Y A383573 Cf. A360290.
%K A383573 nonn
%O A383573 0,2
%A A383573 _Seiichi Manyama_, Apr 30 2025