%I #20 Apr 14 2024 08:50:06
%S 1,7,67,741,8909,113107,1492103,20251945,280978681,3967031839,
%T 56811348235,823250855181,12049087175493,177857857845675,
%U 2644773866954255,39581787842355409,595745692419162737,9011736489133233463,136932249972928786387
%N Expansion of (1/x) * Series_Reversion( x / ( (1+x) * (1+2*x)^3 ) ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(3*(n+1),k) * binomial(n+1,n-k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+2*x)^3))/x)
%o (PARI) a(n) = sum(k=0, n, 2^k*binomial(3*(n+1), k)*binomial(n+1, n-k))/(n+1);
%Y Essentially the same as A243675.
%Y Cf. A034015.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 21 2024