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 A386773 #10 Aug 02 2025 09:57:45
%S A386773 1,12,219,4778,115011,2945982,78764484,2172877458,61393035171,
%T A386773 1767592420152,51672186100899,1529632003964688,45760966837725556,
%U A386773 1381338453812353272,42020564167060633464,1286902432396816483218,39645674268979326240291,1227773019572168363776092
%N A386773 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^2 / (1+2*x)^3 ).
%H A386773 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A386773 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * 3^(n-k) * binomial(3*(n+1),k) * binomial(3*n-k+1,n-k).
%F A386773 a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^3 / (1-3*x)^2 )^(n+1).
%o A386773 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^2/(1+2*x)^3)/x)
%o A386773 (PARI) a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(3*(n+1), k)*binomial(3*n-k+1, n-k))/(n+1);
%Y A386773 Cf. A386722.
%K A386773 nonn
%O A386773 0,2
%A A386773 _Seiichi Manyama_, Aug 02 2025