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 A371837 #12 Apr 08 2024 04:51:04
%S A371837 1,1,3,13,51,201,834,3529,15075,65431,288278,1285263,5799470,26492103,
%T A371837 122432628,572291385,2705760291,12937116213,62542367166,305668511259,
%U A371837 1510080076410,7539381024297,38034307340076,193835252945487,997724306958606,5185731234177001
%N A371837 a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(2*n-3*k-1,n-3*k).
%F A371837 a(n) = [x^n] 1/((1-n*x^3) * (1-x)^n).
%F A371837 a(n) ~ exp(n^(2/3) + n^(1/3)/2 + 1/3) * n^(n/3) / 3. - _Vaclav Kotesovec_, Apr 08 2024
%t A371837 Join[{1}, Table[Sum[n^k*Binomial[2*n-3*k-1,n-1], {k, 0, n/3}], {n, 1, 25}]] (* _Vaclav Kotesovec_, Apr 08 2024 *)
%o A371837 (PARI) a(n) = sum(k=0, n\3, n^k*binomial(2*n-3*k-1, n-3*k));
%Y A371837 Cf. A293574, A371836.
%Y A371837 Cf. A120305, A371827.
%K A371837 nonn
%O A371837 0,3
%A A371837 _Seiichi Manyama_, Apr 08 2024