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 A369300 #20 Feb 15 2024 04:10:42
%S A369300 1,2,7,33,173,962,5589,33546,206359,1294096,8242375,53173095,
%T A369300 346724250,2281555440,15131448440,101038950441,678724811604,
%U A369300 4583483218340,31098830566098,211898222878937,1449322361547669,9947227335902244,68486384818253877
%N A369300 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3)^3 ).
%H A369300 Seiichi Manyama, <a href="/A369300/b369300.txt">Table of n, a(n) for n = 0..1000</a>
%H A369300 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369300 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(3*n-3*k+1,n-3*k).
%F A369300 a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^2 * (1-x^3)^3 )^(n+1). - _Seiichi Manyama_, Feb 14 2024
%o A369300 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x^3)^3)/x)
%o A369300 (PARI) a(n, s=3, t=3, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
%Y A369300 Cf. A369299, A369301.
%Y A369300 Cf. A369297, A369298.
%Y A369300 Cf. A369269.
%K A369300 nonn
%O A369300 0,2
%A A369300 _Seiichi Manyama_, Jan 18 2024