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 A371393 #11 Mar 21 2024 09:20:02
%S A371393 1,7,65,695,8081,99303,1268961,16694295,224617265,3076621127,
%T A371393 42757939841,601443961207,8546453367505,122502619954855,
%U A371393 1769134504184865,25716831677125335,375988660156913265,5525224188936386055,81565308431025658305,1209038650866275440695
%N A371393 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+3*x)^2 ).
%H A371393 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371393 a(n) = (1/(n+1)) * Sum_{k=0..n} 3^k * binomial(2*(n+1),k) * binomial(2*n-k,n-k).
%o A371393 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+3*x)^2)/x)
%o A371393 (PARI) a(n) = sum(k=0, n, 3^k*binomial(2*(n+1), k)*binomial(2*n-k, n-k))/(n+1);
%Y A371393 Cf. A082298, A371394.
%Y A371393 Cf. A064087.
%K A371393 nonn
%O A371393 0,2
%A A371393 _Seiichi Manyama_, Mar 21 2024