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 A368891 #15 Jan 09 2024 08:45:11
%S A368891 1,1,1,4,9,16,61,183,433,1603,5581,15951,59449,225928,738893,2827321,
%T A368891 11387617,41174086,163185805,686315474,2680560361,11035625413,
%U A368891 48086847117,199640217719,853587430801,3836667616201,16739402030989,74206353913480
%N A368891 a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(n-2*k,k).
%F A368891 a(n) = [x^n] 1/(1 - x - n*x^3).
%F A368891 a(n) ~ exp(n^(2/3)/3 + n^(1/3)/18) * n^(n/3) / 3 * (1 + 2/(3*n^(1/3)) + 2/(9*n^(2/3))). - _Vaclav Kotesovec_, Jan 09 2024
%t A368891 Table[HypergeometricPFQ[{1/3 - n/3, 2/3 - n/3, -n/3}, {1/2 - n/2, -n/2}, -27*n/4], {n, 0, 30}] (* _Vaclav Kotesovec_, Jan 09 2024 *)
%o A368891 (PARI) a(n) = sum(k=0, n\3, n^k*binomial(n-2*k, k));
%Y A368891 Cf. A368892, A368893.
%Y A368891 Cf. A171180, A368898.
%Y A368891 Cf. A360748, A368895.
%K A368891 nonn,easy
%O A368891 0,4
%A A368891 _Seiichi Manyama_, Jan 09 2024