A371365 Expansion of (1/x) * Series_Reversion( x * (1-4*x)^3 / (1-3*x) ).

1, 9, 141, 2701, 57513, 1307553, 31083925, 763267077, 19208408721, 492817411705, 12842067417309, 338956669920189, 9042967461581753, 243464712274093713, 6606427290991922277, 180492205687604057013, 4960765361688213527073

Offset: 0

Author

Seiichi Manyama, Mar 19 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A059231, A371364.

Cf. A369023, A371363.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^3/(1-3*x))/x)

PARI

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