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%I #19 Sep 08 2022 08:44:46
%S 1,19531,317886556,5007031143556,78360229974772306,
%T 1224770494838892134806,19138263752352528498478556,
%U 299039198587280398947721603556,4672499438759279108929231093087931,73007841108236063781239140920167306681
%N Gaussian binomial coefficients [ n,6 ] for q = 5.
%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="/A022213/b022213.txt">Table of n, a(n) for n = 6..200</a>
%F G.f.: x^6/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)*(1-15625*x)). - _Vincenzo Librandi_, Aug 10 2016
%F a(n) = Product_{i=1..6} (5^(n-i+1)-1)/(5^i-1), by definition. - _Vincenzo Librandi_, Aug 10 2016
%t Table[QBinomial[n, 6, 5], {n, 6, 20}] (* _Vincenzo Librandi_, Aug 10 2016 *)
%o (Sage) [gaussian_binomial(n,6,5) for n in range(6,16)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=6; q:=5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 10 2016
%o (PARI) r=6; q=5; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 04 2018
%K nonn,easy
%O 6,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 10 2016
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