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A370274
Coefficient of x^n in the expansion of 1/( (1-x) * (1-x^3)^2 )^n.
1
1, 1, 3, 16, 67, 276, 1212, 5391, 24003, 107719, 486728, 2208735, 10059868, 45970367, 210657177, 967636566, 4454109123, 20540731356, 94882599285, 438931979661, 2033217678792, 9429562243530, 43779688919145, 203463271733010, 946445226206940, 4406251540834026
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(2*n-3*k-1,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) * (1-x^3)^2 ). See A369296.
PROG
(PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));
CROSSREFS
Cf. A369296.
Sequence in context: A000269 A378406 A370248 * A015524 A012279 A037098
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 13 2024
STATUS
approved