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 A369299 #20 Feb 15 2024 04:11:37
%S A369299 1,1,2,8,29,105,417,1719,7181,30603,132736,582790,2585352,11575613,
%T A369299 52237278,237328704,1084701387,4983867447,23007263941,106658256768,
%U A369299 496336303014,2317687534865,10856677523580,51001805706435,240225121539000,1134240896062656,5367428039668751
%N A369299 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x^3)^3 ).
%H A369299 Seiichi Manyama, <a href="/A369299/b369299.txt">Table of n, a(n) for n = 0..1000</a>
%H A369299 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369299 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(2*n-3*k,n-3*k).
%F A369299 a(n) = (1/(n+1)) * [x^n] 1/( (1-x) * (1-x^3)^3 )^(n+1). - _Seiichi Manyama_, Feb 14 2024
%o A369299 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x^3)^3)/x)
%o A369299 (PARI) a(n, s=3, t=3, u=1) = 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 A369299 Cf. A369300, A369301.
%Y A369299 Cf. A063030, A369296.
%Y A369299 Cf. A369268.
%K A369299 nonn
%O A369299 0,3
%A A369299 _Seiichi Manyama_, Jan 18 2024