cp's OEIS Frontend

A022200 Gaussian binomial coefficients [ n,9 ] for q = 3.

%I A022200 #19 Sep 08 2022 08:44:46
%S A022200 1,29524,653757313,13362799477720,266307564861468823,
%T A022200 5263390747480701708292,103741619611085612124067759,
%U A022200 2042880353039758115797506899680,40216143252770054194345243936096486,791614563787525746761491781638123230424
%N A022200 Gaussian binomial coefficients [ n,9 ] for q = 3.
%D A022200 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022200 Vincenzo Librandi, <a href="/A022200/b022200.txt">Table of n, a(n) for n = 9..200</a>
%F A022200 G.f.: x^9/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)*(1-2187*x)*(1-6561*x)*(1-19683*x)). - _Vincenzo Librandi_, Aug 10 2016
%F A022200 a(n) = Product_{i=1..9} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 10 2016
%t A022200 Table[QBinomial[n, 9, 3], {n, 9, 20}] (* _Vincenzo Librandi_, Aug 10 2016 *)
%o A022200 (Sage) [gaussian_binomial(n,9,3) for n in range(9,19)] # _Zerinvary Lajos_, May 25 2009
%o A022200 (Magma)  r:=9; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 10 2016
%o A022200 (PARI) r=9; q=3; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 01 2018
%K A022200 nonn
%O A022200 9,2
%A A022200 _N. J. A. Sloane_
%E A022200 Offset changed by _Vincenzo Librandi_, Aug 10 2016