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A372378
Expansion of (1/x) * Series_Reversion( x / (1+x+x^3)^3 ).
3
1, 3, 12, 58, 315, 1836, 11202, 70587, 455715, 2998687, 20037408, 135597168, 927403927, 6400393314, 44516211906, 311719939251, 2195772726315, 15548558852085, 110617749092928, 790281473092740, 5667380226502698, 40782402908527488, 294388014805470744
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+3,k) * binomial(3*n-k+3,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=0) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
CROSSREFS
Cf. A372374.
Sequence in context: A038177 A163047 A369616 * A369594 A369403 A291488
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 29 2024
STATUS
approved