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 A386774 #12 Aug 02 2025 09:58:35
%S A386774 1,17,439,13513,458196,16518407,621247194,24099952473,957294067516,
%T A386774 38741943503972,1591753835634799,66219447135668383,
%U A386774 2783826043226606236,118078452737821009962,5047034289902290964004,217173909723115943823993,9400092428228971114597356
%N A386774 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^3 / (1+2*x)^4 ).
%H A386774 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A386774 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * 3^(n-k) * binomial(4*(n+1),k) * binomial(4*n-k+2,n-k).
%F A386774 a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^4 / (1-3*x)^3 )^(n+1).
%o A386774 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^3/(1+2*x)^4)/x)
%o A386774 (PARI) a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(4*(n+1), k)*binomial(4*n-k+2, n-k))/(n+1);
%Y A386774 Cf. A386723, A386768, A386771.
%K A386774 nonn
%O A386774 0,2
%A A386774 _Seiichi Manyama_, Aug 02 2025