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%I #21 Sep 08 2022 08:44:46
%S 1,3906,12714681,40053706056,125368356709806,391901483074853556,
%T 1224770494838892134806,3827456772141158994166056,
%U 11960833022875371081037525431,37377622327704219905090668384806,116805081731088587940522831693775431
%N Gaussian binomial coefficients [ n,5 ] 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="/A022212/b022212.txt">Table of n, a(n) for n = 5..200</a>
%F G.f.: x^5/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)). - _Vincenzo Librandi_, Aug 10 2016
%F a(n) = Product_{i=1..5} (5^(n-i+1)-1)/(5^i-1), by definition. - _Vincenzo Librandi_, Aug 10 2016
%t QBinomial[Range[5,15],5,5] (* _Harvey P. Dale_, Oct 05 2011 *)
%t Table[QBinomial[n, 5, 5], {n, 5, 20}] (* _Vincenzo Librandi_, Aug 10 2016 *)
%o (Sage) [gaussian_binomial(n,5,5) for n in range(5,14)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=5; 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=5; 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 5,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 10 2016
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