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 A379547 #18 Aug 25 2025 10:16:35
%S A379547 1,10,141,2318,41586,789404,15588677,316957910,6591000606,
%T A379547 139521610540,2996554128002,65135251885164,1430214488595340,
%U A379547 31676376789702720,706819317765805461,15874751837921964646,358585244386746378166,8141109472248910295708
%N A379547 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^2 * (1+2*x)^4 ) ).
%H A379547 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A379547 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(4*(n+1),k) * binomial(2*(n+1),n-k).
%F A379547 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(n+1,k) * binomial(5*(n+1)-k,n-2*k).
%F A379547 a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 * (1+2*x)^4 )^(n+1).
%t A379547 CoefficientList[InverseSeries[Series[x / ( (1+x)^2 * (1+2*x)^4 ),{x,0,18}],x]/x,x] (* _Stefano Spezia_, Aug 25 2025 *)
%o A379547 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+2*x)^4))/x)
%o A379547 (PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(n+1, k)*binomial(5*(n+1)-k, n-2*k))/(n+1);
%Y A379547 Cf. A003168, A371406, A379546.
%K A379547 nonn,changed
%O A379547 0,2
%A A379547 _Seiichi Manyama_, Dec 25 2024