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 A386723 #9 Jul 31 2025 10:06:30
%S A386723 1,11,175,3275,67156,1460237,33073930,771961835,18437940220,
%T A386723 448483875596,11071403236807,276675755470349,6985664542196380,
%U A386723 177932236341440270,4566561255466298500,117974930924420353835,3065563791639454312492,80069021664742889373380
%N A386723 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1+2*x)^4 ).
%H A386723 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A386723 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(4*(n+1),k) * binomial(4*n-k+2,n-k).
%F A386723 a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^4 / (1-x)^3 )^(n+1).
%o A386723 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1+2*x)^4)/x)
%o A386723 (PARI) a(n) = sum(k=0, n, 2^k*binomial(4*(n+1), k)*binomial(4*n-k+2, n-k))/(n+1);
%Y A386723 Cf. A371391, A386722.
%Y A386723 Cf. A386719.
%K A386723 nonn
%O A386723 0,2
%A A386723 _Seiichi Manyama_, Jul 31 2025