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 A371754 #11 Oct 19 2024 16:29:27
%S A371754 1,3,15,85,505,3081,19125,120173,761995,4865697,31244029,201544551,
%T A371754 1305039209,8477521051,55221311565,360559717807,2359123470971,
%U A371754 15463951609491,101530816122729,667587477393509,4395294402200983,28972295880583861,191181607835416543
%N A371754 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-2*k,n-3*k).
%F A371754 a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(2*n)).
%F A371754 a(n) ~ 3^(3*n + 5/2) / (17 * sqrt(Pi*n) * 2^(2*n)). - _Vaclav Kotesovec_, Apr 05 2024
%t A371754 Table[Sum[Binomial[3n-2k,n-3k],{k,0,Floor[n/3]}],{n,0,30}] (* _Harvey P. Dale_, Oct 19 2024 *)
%o A371754 (PARI) a(n) = sum(k=0, n\3, binomial(3*n-2*k, n-3*k));
%Y A371754 Cf. A144904, A371755, A371756.
%Y A371754 Cf. A066380, A371742.
%K A371754 nonn
%O A371754 0,2
%A A371754 _Seiichi Manyama_, Apr 05 2024