A372373 Coefficient of x^n in the expansion of ( (1+x+x^3)^3 / (1+x)^2 )^n.

1, 1, 1, 10, 37, 91, 334, 1366, 4645, 15967, 59951, 220782, 792946, 2906554, 10770082, 39629440, 145966549, 540943231, 2006762563, 7443051014, 27661527427, 102980882455, 383639407570, 1430429881122, 5339465251426, 19947662875216, 74573064834646

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(3*n,k) * binomial(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)^2 / (1+x+x^3)^3 ). See A372377.

Prog

(PARI) a(n, s=3, t=3, u=-2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));

Crossrefs

Cf. A372372, A372374.

Cf. A372377.

Sequence in context: A212795 A227695 A247792 * A096000 A047672 A200872

Adjacent sequences: A372370 A372371 A372372 * A372374 A372375 A372376

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved