A371363 Expansion of (1/x) * Series_Reversion( x * (1-3*x)^3 / (1-2*x) ).

1, 7, 85, 1261, 20788, 365845, 6731758, 127938625, 2491921516, 49480794460, 997897366717, 20384025765619, 420869454302620, 8769197604091246, 184151509243984300, 3893585866824069577, 82817275938125471548, 1770880435886367151060

Offset: 0

Author

Seiichi Manyama, Mar 19 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A007564, A371362.

Cf. A369023, A371365.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^3/(1-2*x))/x)

PARI

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