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 A360811 #15 Feb 22 2024 02:17:11
%S A360811 1,1,1,1,2,5,10,18,38,91,211,472,1108,2754,6881,17101,43443,113565,
%T A360811 300142,797191,2147414,5883976,16293712,45471429,128285353,366266188,
%U A360811 1055534118,3066483484,8989837397,26602652605,79370560477,238606427241,722973445270
%N A360811 Expansion of Sum_{k>=0} ( x / (1 - k * x^3) )^k.
%H A360811 Robert Israel, <a href="/A360811/b360811.txt">Table of n, a(n) for n = 0..1000</a>
%F A360811 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^k * binomial(n-2*k-1,k).
%p A360811 N:= 100:
%p A360811 F:= 1 + add((x/(1-k*x^3))^k, k=1..N):
%p A360811 S:= series(F,x,N+1):
%p A360811 seq(coeff(S,x,k),k=0..N); # _Robert Israel_, Feb 21 2024
%o A360811 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k*x^3))^k))
%o A360811 (PARI) a(n) = sum(k=0, n\3, (n-3*k)^k*binomial(n-2*k-1, k));
%Y A360811 Cf. A324158, A360783.
%K A360811 nonn
%O A360811 0,5
%A A360811 _Seiichi Manyama_, Feb 21 2023