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 A360709 #11 Feb 17 2023 12:16:00
%S A360709 1,0,0,1,1,1,2,5,13,34,90,247,720,2256,7568,26814,98982,377541,
%T A360709 1484254,6021789,25271173,109850447,494355359,2298362532,11008133629,
%U A360709 54175202125,273460921605,1414449612648,7494262602464,40669492399396
%N A360709 Expansion of Sum_{k>=0} (x^3 / (1 - k*x))^k.
%H A360709 Winston de Greef, <a href="/A360709/b360709.txt">Table of n, a(n) for n = 0..692</a>
%F A360709 a(n) = Sum_{k=1..floor(n/3)} k^(n-3*k) * binomial(n-2*k-1,k-1) for n > 0.
%o A360709 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x^3/(1-k*x))^k))
%o A360709 (PARI) a(n) = if(n==0, 1, sum(k=1, n\3, k^(n-3*k)*binomial(n-2*k-1, k-1)));
%Y A360709 Cf. A080108, A360708.
%Y A360709 Cf. A078012, A360707.
%K A360709 nonn
%O A360709 0,7
%A A360709 _Seiichi Manyama_, Feb 17 2023