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 A383581 #16 May 02 2025 08:00:38
%S A383581 1,2,6,21,74,270,1005,3788,14418,55289,213270,826614,3216629,12558928,
%T A383581 49175136,193023965,759299438,2992534344,11813985377,46709675040,
%U A383581 184928644350,733047010709,2908981549006,11555513379450,45945148281437,182835149061920,728149606630164
%N A383581 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(2*(n-3*k),n-3*k).
%H A383581 Vincenzo Librandi, <a href="/A383581/b383581.txt">Table of n, a(n) for n = 0..400</a>
%F A383581 G.f.: 1/sqrt((1 - x^3) * (1 - x^3 - 4*x)).
%t A383581 Table[Sum[Binomial[n-2*k,k]* Binomial[2*(n-3*k),n-3*k],{k,0,Floor[n/3]}],{n,0,30}] (* _Vincenzo Librandi_, May 02 2025 *)
%o A383581 (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(2*(n-3*k), n-3*k));
%o A383581 (Magma) [&+[Binomial(n-2*k,k) * Binomial(2*(n-3*k),n-3*k): k in [0..n div 3]]: n in [0..25]]; // _Vincenzo Librandi_, May 02 2025
%Y A383581 Cf. A026375, A383573, A383582.
%Y A383581 Cf. A376791, A383571.
%Y A383581 Cf. A360291.
%K A383581 nonn
%O A383581 0,2
%A A383581 _Seiichi Manyama_, Apr 30 2025