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 A369630 #9 Jan 28 2024 09:19:38
%S A369630 1,1,2,6,20,70,255,960,3707,14598,58395,236626,969275,4007041,
%T A369630 16696822,70053159,295691622,1254772103,5349978803,22907982780,
%U A369630 98466168572,424713570017,1837717336614,7974744620620,34698200181696,151341512079231,661590732178716
%N A369630 Expansion of (1/x) * Series_Reversion( x * (1/(1+x^3) - x) ).
%H A369630 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369630 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n-3*k+1,k) * binomial(2*n-3*k,n-3*k).
%o A369630 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x^3)-x))/x)
%o A369630 (PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k+1, k)*binomial(2*n-3*k,n-3*k))/(n+1);
%Y A369630 Cf. A007863, A199874, A369631.
%Y A369630 Cf. A226974.
%K A369630 nonn
%O A369630 0,3
%A A369630 _Seiichi Manyama_, Jan 28 2024