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%I #18 Sep 08 2022 08:44:46
%S 1,9331,74630671,583026951031,4537117983992551,35285166561510069127,
%T 274383335413146060060487,2133612436978999661759040967,
%U 16590980186519640252690843276487,129011474730413928552335877184470727
%N Gaussian binomial coefficients [ n,5 ] 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="/A022223/b022223.txt">Table of n, a(n) for n = 5..200</a>
%F G.f.: x^5/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)*(1-7776*x)). - _Vincenzo Librandi_, Aug 12 2016
%F a(n) = Product_{i=1..5} (6^(n-i+1)-1)/(6^i-1), by definition. - _Vincenzo Librandi_, Aug 12 2016
%t Table[QBinomial[n, 5, 6], {n, 5, 20}] (* _Vincenzo Librandi_, Aug 12 2016 *)
%o (Sage) [gaussian_binomial(n,5,6) for n in range(5,15)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=5; 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=5; q=6; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 07 2018
%K nonn,easy
%O 5,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 12 2016
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