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 A369621 #9 Jan 28 2024 09:19:26
%S A369621 1,1,2,6,18,57,191,660,2334,8417,30831,114380,428915,1623143,6190876,
%T A369621 23774613,91849846,356735941,1392091107,5455425618,21460947111,
%U A369621 84717452192,335479515201,1332327233554,5305235886691,21176621863427,84720103674498
%N A369621 Expansion of (1/x) * Series_Reversion( x / (1/(1-x) + x^3) ).
%H A369621 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369621 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(2*n-4*k,n-3*k).
%o A369621 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)+x^3))/x)
%o A369621 (PARI) a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(2*n-4*k, n-3*k))/(n+1);
%Y A369621 Cf. A369622, A369623.
%K A369621 nonn
%O A369621 0,3
%A A369621 _Seiichi Manyama_, Jan 27 2024