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

%I A022197 #20 Sep 08 2022 08:44:46
%S A022197 1,1093,896260,678468820,500777836042,366573514642546,
%T A022197 267598665689058580,195168545232713290660,142299528422960399756323,
%U A022197 103741619611085612124067759,75628919722004322604209288760,55133793282290501540016988429720
%N A022197 Gaussian binomial coefficients [ n,6 ] for q = 3.
%H A022197 Vincenzo Librandi, <a href="/A022197/b022197.txt">Table of n, a(n) for n = 6..200</a>
%F A022197 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 A022197 a(n) = Product_{i=1..6} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 07 2016
%t A022197 Table[QBinomial[n, 6, 3], {n, 6, 20}] (* _Vincenzo Librandi_, Aug 07 2016 *)
%o A022197 (Sage) [gaussian_binomial(n,6,3) for n in range(6,18)] # _Zerinvary Lajos_, May 25 2009
%o A022197 (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 A022197 (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 A022197 nonn,easy
%O A022197 6,2
%A A022197 _N. J. A. Sloane_
%E A022197 Offset changed by _Vincenzo Librandi_, Aug 07 2016