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 A369401 #13 Feb 16 2024 09:53:57
%S A369401 1,1,1,4,16,46,139,511,1891,6707,24366,91840,348236,1320309,5056414,
%T A369401 19565036,76077330,296994727,1165438921,4594915664,18181401268,
%U A369401 72176250259,287450966807,1148178877918,4598148937702,18458646079181,74267340207247
%N A369401 Expansion of (1/x) * Series_Reversion( x / (1+x) * (1-x^3)^3 ).
%H A369401 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369401 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(n+1,n-3*k).
%F A369401 a(n) = (1/(n+1)) * [x^n] ( (1+x) / (1-x^3)^3 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A369401 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)*(1-x^3)^3)/x)
%o A369401 (PARI) a(n, s=3, t=3, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial(u*(n+1), n-s*k))/(n+1);
%Y A369401 Cf. A369402, A369403.
%Y A369401 Cf. A369299, A370216.
%K A369401 nonn
%O A369401 0,4
%A A369401 _Seiichi Manyama_, Jan 22 2024