%I #12 Apr 29 2024 09:06:31

%S 1,3,12,58,315,1836,11202,70587,455715,2998687,20037408,135597168,

%T 927403927,6400393314,44516211906,311719939251,2195772726315,

%U 15548558852085,110617749092928,790281473092740,5667380226502698,40782402908527488,294388014805470744

%N Expansion of (1/x) * Series_Reversion( x / (1+x+x^3)^3 ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+3,k) * binomial(3*n-k+3,n-3*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^3)^3)/x)

%o (PARI) a(n, s=3, t=3, u=0) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);

%Y Cf. A372376, A372377.

%Y Cf. A372374.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 29 2024