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 A386722 #11 Jul 31 2025 10:06:33
%S A386722 1,8,91,1214,17731,274526,4426948,73561238,1250803171,21659155028,
%T A386722 380638861219,6771681469952,121716110229364,2207040281944856,
%U A386722 40323735229993336,741613603443652214,13718779315483616227,255086483631977702096,4764893748897482791633,89373590789286772582334
%N A386722 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+2*x)^3 ).
%H A386722 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A386722 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(3*(n+1),k) * binomial(3*n-k+1,n-k).
%F A386722 a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^3 / (1-x)^2 )^(n+1).
%o A386722 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+2*x)^3)/x)
%o A386722 (PARI) a(n) = sum(k=0, n, 2^k*binomial(3*(n+1), k)*binomial(3*n-k+1, n-k))/(n+1);
%Y A386722 Cf. A371391, A386723.
%Y A386722 Cf. A385320.
%K A386722 nonn
%O A386722 0,2
%A A386722 _Seiichi Manyama_, Jul 31 2025