login
Gaussian binomial coefficients [ n,8 ] for q = 6.
1

%I #25 Sep 08 2022 08:44:46

%S 1,2015539,3482055254095,5875718100153221815,

%T 9876570938882852540717095,16590980186519640252690843276487,

%U 27867073064694433516284053323814269063,46806148995565935663430369990805328306755335,78616403557485470161203927752846473114607475506695

%N Gaussian binomial coefficients [ n,8 ] 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="/A022226/b022226.txt">Table of n, a(n) for n = 8..170</a>

%F G.f.: -x^8/((x-1)*(6*x-1)*(36*x-1)*(216*x-1)*(1296*x-1)*(7776*x-1)*(46656*x-1)* (279936*x-1)*(1679616*x-1)). - _Harvey P. Dale_, Jun 24 2011

%F a(n) = Product_{i=1..8} (6^(n-i+1)-1)/(6^i-1), by definition. - _Vincenzo Librandi_, Aug 12 2016

%t QBinomial[Range[8,20],8,6] (* _Harvey P. Dale_, Jun 24 2011 *)

%t Table[QBinomial[n, 8, 6], {n, 8, 20}] (* _Vincenzo Librandi_, Aug 12 2016 *)

%o (Sage) [gaussian_binomial(n,8,6) for n in range(8,15)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=8; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 12 2016

%o (PARI) r=8; 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 8,2

%A _N. J. A. Sloane_

%E More terms from _Harvey P. Dale_, Jun 24 2011

%E Offset changed by _Vincenzo Librandi_, Aug 12 2016