A371385 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^3 / (1-x) ).

1, 8, 109, 1808, 33283, 653696, 13419460, 284479136, 6179728951, 136842057800, 3077436307141, 70095952722752, 1613743723323028, 37490308916974496, 877802418598193488, 20693109628871653184, 490732756789852308223, 11699199238845493854872

Offset: 0

Author

Seiichi Manyama, Mar 20 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A107841, A371380.

Cf. A371363.

Programs

PARI

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

PARI

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(3*n+k+2,k) * binomial(3*n+1,n-k).