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 A386772 #9 Aug 02 2025 09:57:49
%S A386772 1,7,74,943,13326,200982,3169524,51633343,862145126,14677296082,
%T A386772 253802667724,4445613370118,78712814985676,1406483499289932,
%U A386772 25330499214488424,459331317209458143,8379478714912128726,153679237018626276282,2831839422052964444124
%N A386772 Expansion of (1/x) * Series_Reversion( x * (1-3*x) / (1+2*x)^2 ).
%H A386772 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A386772 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * 3^(n-k) * binomial(2*(n+1),k) * binomial(2*n-k,n-k).
%F A386772 a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^2 / (1-3*x) )^(n+1).
%o A386772 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)/(1+2*x)^2)/x)
%o A386772 (PARI) a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(2*(n+1), k)*binomial(2*n-k, n-k))/(n+1);
%Y A386772 Cf. A371391.
%K A386772 nonn
%O A386772 0,2
%A A386772 _Seiichi Manyama_, Aug 02 2025