A372372 Coefficient of x^n in the expansion of ( (1+x+x^3)^3 / (1+x) )^n.

1, 2, 6, 29, 154, 792, 4047, 20967, 110058, 582257, 3096516, 16539690, 88684291, 477080671, 2573652045, 13917256254, 75417513498, 409447753305, 2226602481387, 12126317466294, 66129124080804, 361059693982863, 1973513103986606, 10797777359289435

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*n,k) * binomial(2*n-k,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+x^3)^3 ). See A372376.

Prog

(PARI) a(n, s=3, t=3, u=-1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));

Crossrefs

Cf. A372373, A372374.

Cf. A372376.

Sequence in context: A284594 A027109 A348764 * A107375 A302863 A370217

Adjacent sequences: A372369 A372370 A372371 * A372373 A372374 A372375

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved