A367462 Expansion of (1/x) * Series_Reversion( x / (1+x+x^3/(1+x)) ).

1, 1, 1, 2, 4, 7, 14, 30, 62, 131, 287, 629, 1385, 3096, 6967, 15735, 35782, 81823, 187781, 432689, 1000919, 2322584, 5405094, 12614260, 29512587, 69205602, 162634994, 382961435, 903431963, 2134945637, 5053385429, 11979405642, 28438444486, 67601886687

Offset: 0

Author

Seiichi Manyama, Jan 26 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A126042.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^3/(1+x)))/x)

PARI

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

Formula

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