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 A386769 #14 Aug 03 2025 11:02:14
%S A386769 1,8,89,1162,16646,253218,4016769,65713602,1100773166,18786755128,
%T A386769 325518195674,5711193510092,101260078423336,1811480526001238,
%U A386769 32657053453306929,592701233703282882,10820725155122336406,198584549759713158048,3661487133197990007534
%N A386769 Expansion of (1/x) * Series_Reversion( x * (1-2*x) / (1+3*x)^2 ).
%H A386769 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A386769 a(n) = (1/(n+1)) * Sum_{k=0..n} 3^k * 2^(n-k) * binomial(2*(n+1),k) * binomial(2*n-k,n-k).
%F A386769 a(n) = (1/(n+1)) * [x^n] ( (1+3*x)^2 / (1-2*x) )^(n+1).
%F A386769 D-finite with recurrence 2*(n+1)*a(n) +(-31*n+29)*a(n-1) +90*(-2*n+1)*a(n-2)=0. - _R. J. Mathar_, Aug 03 2025
%o A386769 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)/(1+3*x)^2)/x)
%o A386769 (PARI) a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(2*(n+1), k)*binomial(2*n-k, n-k))/(n+1);
%Y A386769 Cf. A064063, A386763.
%K A386769 nonn
%O A386769 0,2
%A A386769 _Seiichi Manyama_, Aug 02 2025