A371385 - OEIS

%I #8 Mar 21 2024 09:19:16

%S 1,8,109,1808,33283,653696,13419460,284479136,6179728951,136842057800,

%T 3077436307141,70095952722752,1613743723323028,37490308916974496,

%U 877802418598193488,20693109628871653184,490732756789852308223,11699199238845493854872

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

%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+k+2,k) * binomial(3*n+1,n-k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^3/(1-x))/x)

%o (PARI) a(n) = sum(k=0, n, 2^k*binomial(3*n+k+2, k)*binomial(3*n+1, n-k))/(n+1);

%Y Cf. A107841, A371380.

%Y Cf. A371363.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 20 2024