A022197 Gaussian binomial coefficients [ n,6 ] for q = 3.

1, 1093, 896260, 678468820, 500777836042, 366573514642546, 267598665689058580, 195168545232713290660, 142299528422960399756323, 103741619611085612124067759, 75628919722004322604209288760, 55133793282290501540016988429720

Offset: 6

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 6..200

Programs

Magma

r:=6; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 07 2016

Mathematica

Table[QBinomial[n, 6, 3], {n, 6, 20}] (* Vincenzo Librandi, Aug 07 2016 *)

PARI

r=6; q=3; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, May 30 2018

Sage

[gaussian_binomial(n,6,3) for n in range(6,18)] # Zerinvary Lajos, May 25 2009

Formula

G.f.: x^6/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)). - Vincenzo Librandi, Aug 07 2016

a(n) = Product_{i=1..6} (3^(n-i+1)-1)/(3^i-1), by definition. - Vincenzo Librandi, Aug 07 2016

Extensions

Offset changed by Vincenzo Librandi, Aug 07 2016