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 A369123 #11 Jan 14 2024 08:56:01
%S A369123 1,2,6,20,68,224,672,1584,880,-22880,-215072,-1414400,-8012032,
%T A369123 -41344000,-198120448,-884348160,-3640426752,-13403384320,
%U A369123 -40424947200,-65476561920,329862128640,4603911045120,35276325027840,221747978649600,1244854463643648
%N A369123 Expansion of (1/x) * Series_Reversion( x * ((1-x)^2+x^2) ).
%H A369123 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369123 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+k,k) * binomial(3*n+1,n-2*k).
%o A369123 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2+x^2))/x)
%o A369123 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+k, k)*binomial(3*n+1, n-2*k))/(n+1);
%Y A369123 Cf. A097188, A369124, A369125.
%K A369123 sign
%O A369123 0,2
%A A369123 _Seiichi Manyama_, Jan 13 2024