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A370217
Coefficient of x^n in the expansion of ( (1+x)^2 / (1-x^3)^3 )^n.
1
1, 2, 6, 29, 166, 927, 5055, 27687, 153702, 861950, 4862481, 27543111, 156571951, 892919445, 5106591405, 29275176204, 168181755750, 967967551701, 5580293663274, 32217589171489, 186253647533841, 1078046039503182, 6246592211179337, 36231065957573793
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k-1,k) * binomial(2*n,n-3*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3)^3 ). See A369402.
PROG
(PARI) a(n, s=3, t=3, u=2) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));
CROSSREFS
Cf. A369402.
Sequence in context: A372372 A107375 A302863 * A020126 A124529 A370456
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 12 2024
STATUS
approved