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 A369489 #10 Jan 24 2024 08:00:30
%S A369489 1,1,2,7,26,98,387,1589,6688,28676,124880,550926,2456831,11056693,
%T A369489 50152457,229050621,1052393802,4861062466,22559964766,105144660498,
%U A369489 491922058878,2309456782464,10876596029574,51372213424194,243283513468707,1154929327702775,5495105429597720
%N A369489 Expansion of (1/x) * Series_Reversion( x / (1-x) * (1-x-x^3)^2 ).
%H A369489 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369489 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(2*n-2*k,n-3*k).
%o A369489 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1-x)*(1-x-x^3)^2)/x)
%o A369489 (PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t-u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y A369489 Cf. A368962, A368966, A368968, A369011.
%Y A369489 Cf. A054514, A369486.
%K A369489 nonn
%O A369489 0,3
%A A369489 _Seiichi Manyama_, Jan 24 2024