A370621 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^2)^3 )^n.

1, 2, 16, 119, 948, 7732, 64231, 540311, 4588076, 39244106, 337624066, 2918384229, 25325306031, 220497804256, 1925231880973, 16850975055139, 147807248526268, 1298926641563548, 11434042768577866, 100800817171002817, 889839745865544598

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(3*n-k-1,n-2*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-x^2)^3 / (1-x) ). See A369487.

Mathematica

a[n_]:=SeriesCoefficient[((1-x)/(1-x-x^2)^3)^n, {x, 0, n}]; Array[a, 21, 0] (* Stefano Spezia, May 01 2024 *)

Prog

(PARI) a(n, s=2, t=3, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));

Crossrefs

Cf. A370620, A370622, A370623.

Cf. A369487.

Sequence in context: A159324 A088755 A136782 * A112710 A046105 A086854

Adjacent sequences: A370618 A370619 A370620 * A370622 A370623 A370624

Keyword

nonn

Author

Seiichi Manyama, May 01 2024

Status

approved