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 A379546 #14 Dec 25 2024 09:17:12
%S A379546 1,8,89,1150,16190,240966,3729185,59404934,967608590,16041857672,
%T A379546 269807678442,4592326407908,78954271935856,1369136489157250,
%U A379546 23918810207745777,420575805001923782,7437459126200243030,132190772588551036800,2360148586461490077870
%N A379546 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^3 ) ).
%H A379546 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A379546 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(3*(n+1),k) * binomial(2*(n+1),n-k).
%F A379546 a(n) = A371669(n+1)/2 = (1/(n+1)) * Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(n+1,k) * binomial(4*(n+1)-k,n-2*k).
%F A379546 a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 * (1+2*x)^3 )^(n+1).
%o A379546 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+2*x)^3))/x)
%o A379546 (PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(n+1, k)*binomial(4*(n+1)-k, n-2*k))/(n+1);
%Y A379546 Cf. A003168, A371406, A379547.
%Y A379546 Cf. A371398, A379522.
%Y A379546 Cf. A371669.
%K A379546 nonn
%O A379546 0,2
%A A379546 _Seiichi Manyama_, Dec 25 2024