A369623 Expansion of (1/x) * Series_Reversion( x / (1/(1-x)^3 + x^3) ).

1, 3, 15, 92, 624, 4509, 34033, 265164, 2116560, 17219068, 142252608, 1190173956, 10064038469, 85873044573, 738446318232, 6393218956733, 55680130965252, 487488352916496, 4288083926110045, 37878037865662422, 335859658273133355, 2988274511990407436

Offset: 0

Author

Seiichi Manyama, Jan 27 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369621, A369622.

Cf. A369600.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(4*n-6*k+2, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(4*n-6*k+2,n-3*k).