%I #20 Sep 08 2022 08:44:46

%S 1,1093,896260,678468820,500777836042,366573514642546,

%T 267598665689058580,195168545232713290660,142299528422960399756323,

%U 103741619611085612124067759,75628919722004322604209288760,55133793282290501540016988429720

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

%H Vincenzo Librandi, <a href="/A022197/b022197.txt">Table of n, a(n) for n = 6..200</a>

%F 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

%F a(n) = Product_{i=1..6} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 07 2016

%t Table[QBinomial[n, 6, 3], {n, 6, 20}] (* _Vincenzo Librandi_, Aug 07 2016 *)

%o (Sage) [gaussian_binomial(n,6,3) for n in range(6,18)] # _Zerinvary Lajos_, May 25 2009

%o (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

%o (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

%K nonn,easy

%O 6,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 07 2016