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Gaussian binomial coefficients [ n,12 ] for q = 6.
1

%I #21 Sep 08 2022 08:44:46

%S 1,2612138803,5848516394205967951,12790160886494733304250601655,

%T 27862895440026036935366271191556077095,

%U 60659259454351187375733691191139808969963672263,132044834674141024683472683631781840882298387938848321159

%N Gaussian binomial coefficients [ n,12 ] for q = 6.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

%H Vincenzo Librandi, <a href="/A022230/b022230.txt">Table of n, a(n) for n = 12..120</a>

%F a(n) = Product_{i=1..12} (6^(n-i+1)-1)/(6^i-1), by definition. - _Vincenzo Librandi_, Aug 06 2016

%F G.f.: x^12/Product_{k=0..12} (1 - 6^k*x). - _Ilya Gutkovskiy_, Aug 06 2016

%t Table[QBinomial[n, 12, 6], {n, 12, 20}] (* _Vincenzo Librandi_, Aug 06 2016 *)

%o (Sage) [gaussian_binomial(n,12,6) for n in range(12,19)] # _Zerinvary Lajos_, May 28 2009

%o (Magma) r:=12; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 06 2016

%o (PARI) r=12; q=6; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 13 2018

%K nonn,easy

%O 12,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 06 2016