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 A369400 #13 Feb 16 2024 09:54:01
%S A369400 1,2,5,16,62,264,1172,5342,24905,118410,572167,2801354,13865237,
%T A369400 69258500,348698784,1767724720,9015710574,46227736956,238159867070,
%U A369400 1232206495528,6399778252336,33354634754364,174390047681360,914414985920664,4807481173042396
%N A369400 Expansion of (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3)^2 ).
%H A369400 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369400 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(2*n+2,n-3*k).
%F A369400 a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 / (1-x^3)^2 )^(n+1). - _Seiichi Manyama_, Feb 16 2024
%o A369400 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)^2*(1-x^3)^2)/x)
%o A369400 (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial(u*(n+1), n-s*k))/(n+1);
%Y A369400 Cf. A396298.
%K A369400 nonn
%O A369400 0,2
%A A369400 _Seiichi Manyama_, Jan 22 2024