cp's OEIS Frontend

A022198 Gaussian binomial coefficients [ n,7 ] for q = 3.

%I A022198 #19 Sep 08 2022 08:44:46
%S A022198 1,3280,8069620,18326727760,40581331447162,89117945389585840,
%T A022198 195168545232713290660,427028776969176679964080,
%U A022198 934054234760012359481199283,2042880353039758115797506899680,4467854961017673003571751798888920
%N A022198 Gaussian binomial coefficients [ n,7 ] for q = 3.
%D A022198 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022198 Vincenzo Librandi, <a href="/A022198/b022198.txt">Table of n, a(n) for n = 7..200</a>
%F A022198 G.f.: x^7/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)*(1-2187*x)). - _Vincenzo Librandi_, Aug 07 2016
%F A022198 a(n) = Product_{i=1..7} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 07 2016
%t A022198 Table[QBinomial[n, 7, 3], {n, 7, 20}] (* _Vincenzo Librandi_, Aug 07 2016 *)
%o A022198 (Sage) [gaussian_binomial(n,7,3) for n in range(7,18)] # _Zerinvary Lajos_, May 25 2009
%o A022198 (Magma) r:=7; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 07 2016
%o A022198 (PARI) r=7; 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 A022198 nonn,easy
%O A022198 7,2
%A A022198 _N. J. A. Sloane_, Jun 14 1998
%E A022198 Offset changed by _Vincenzo Librandi_, Aug 07 2016