A372376 Expansion of (1/x) * Series_Reversion( x * (1+x) / (1+x+x^3)^3 ).

1, 2, 5, 17, 69, 297, 1317, 6008, 28106, 134094, 649610, 3186439, 15795137, 79002875, 398220450, 2020817214, 10315652205, 52934429595, 272901102282, 1412828261100, 7341969856083, 38284412715874, 200255776288357, 1050476288628006, 5524897831049580

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x)/(1+x+x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=-1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);

Crossrefs

Cf. A372377, A372378.

Sequence in context: A027361 A101971 A211387 * A303952 A162037 A319467

Adjacent sequences: A372373 A372374 A372375 * A372377 A372378 A372379

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved