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 A369298 #20 Feb 15 2024 04:25:01
%S A369298 1,2,7,32,163,884,5011,29342,176092,1077384,6695093,42140930,
%T A369298 268108170,1721372836,11138994028,72573587520,475674650717,
%U A369298 3134297846792,20750020222815,137953554890508,920667400056250,6165565645765092,41419898169301995
%N A369298 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3)^2 ).
%H A369298 Peter Bala, <a href="/A251592/a251592.pdf">Fractional iteration of a series inversion operator</a>
%H A369298 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369298 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(3*n-3*k+1,n-3*k).
%F A369298 a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^2 * (1-x^3)^2 )^(n+1). - _Seiichi Manyama_, Feb 14 2024
%o A369298 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x^3)^2)/x)
%o A369298 (PARI) a(n, s=3, t=2, 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 A369298 Cf. A369297, A369300.
%Y A369298 Cf. A369296, A370275.
%K A369298 nonn
%O A369298 0,2
%A A369298 _Seiichi Manyama_, Jan 18 2024