%I #17 Sep 08 2022 08:44:46
%S 1,72559411,4512744117222991,274137535269957102205111,
%T 16588848493045381066264096333351,
%U 1003193244092547201468344847250540706503,60660559425600837230512947639888522210296616583,3667925165214264518763232198536887427772300866095529223
%N Gaussian binomial coefficients [ n,10 ] 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="/A022228/b022228.txt">Table of n, a(n) for n = 10..140</a>
%F G.f.: x^10/((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)*(1-60466176*x)). - _Vincenzo Librandi_, Aug 12 2016
%F a(n) = Product_{i=1..10} (6^(n-i+1)-1)/(6^i-1), by definition. - _Vincenzo Librandi_, Aug 12 2016
%t Table[QBinomial[n, 10, 6], {n, 10, 20}] (* _Vincenzo Librandi_, Aug 12 2016 *)
%o (Sage) [gaussian_binomial(n,10,6) for n in range(10,18)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=10; 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=10; 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 10,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 12 2016