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 A369599 #11 Jan 27 2024 10:31:21
%S A369599 1,2,5,15,54,223,993,4580,21521,102563,495318,2422302,11979965,
%T A369599 59824535,301202673,1527118720,7789673832,39947163395,205835776301,
%U A369599 1065155017623,5533253267649,28844759080896,150846487065730,791163319140664,4160593763997122
%N A369599 Expansion of (1/x) * Series_Reversion( x * (1/(1+x)^2 - x^3) ).
%H A369599 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369599 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(2*n+2*k+2,n-3*k).
%o A369599 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x)^2-x^3))/x)
%o A369599 (PARI) a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(2*n+2*k+2, n-3*k))/(n+1);
%Y A369599 Cf. A198888, A369600.
%Y A369599 Cf. A274378, A274734.
%K A369599 nonn
%O A369599 0,2
%A A369599 _Seiichi Manyama_, Jan 27 2024