A369442 Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x^3)^2) ).

1, 1, 1, 3, 11, 31, 84, 261, 865, 2815, 9131, 30339, 102681, 349376, 1193993, 4111947, 14263137, 49720513, 174040102, 611770893, 2158954383, 7645030641, 27153898487, 96719683491, 345414958227, 1236555046701, 4436564115556, 15950469680836, 57455730349552

Offset: 0

Author

Seiichi Manyama, Jan 23 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A198951.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x^3)^2))/x)

PARI

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

Formula

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