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Gaussian binomial coefficients [ n,9 ] for q = 6.
1

%I #17 Sep 08 2022 08:44:46

%S 1,12093235,125354001240655,1269155234987097152695,

%T 12800037205947411879866507815,129011474730413928552335877184470727,

%U 1300166289917858220549677344211755721874055

%N Gaussian binomial coefficients [ n,9 ] 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="/A022227/b022227.txt">Table of n, a(n) for n = 9..150</a>

%F G.f.: x^9/((1-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)*(1-10077696*x)). - _Vincenzo Librandi_, Aug 12 2016

%F a(n) = Product_{i=1..9} (6^(n-i+1)-1)/(6^i-1), by definition. - _Vincenzo Librandi_, Aug 12 2016

%t Table[QBinomial[n, 9, 6], {n, 9, 20}] (* _Vincenzo Librandi_, Aug 12 2016 *)

%o (Sage) [gaussian_binomial(n,9,6) for n in range(9,16)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=9; 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=9; 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 9,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 12 2016