A370274 Coefficient of x^n in the expansion of 1/( (1-x) * (1-x^3)^2 )^n.

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

Links

Table of n, a(n) for n=0..25.

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: A248016 A000269 A370248 * A015524 A012279 A037098

Adjacent sequences: A370271 A370272 A370273 * A370275 A370276 A370277

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved