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A372376
Expansion of (1/x) * Series_Reversion( x * (1+x) / (1+x+x^3)^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
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
Sequence in context: A027361 A101971 A211387 * A303952 A162037 A319467
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 29 2024
STATUS
approved