%I #19 Sep 08 2022 08:44:46
%S 1,488281,198682027181,78236053707784181,30609934249224268600431,
%T 11960833022875371081037525431,4672499438759279108929231093087931,
%U 1825218456001772231793929085435472462931,712977784594148279816735342927316866304884806
%N Gaussian binomial coefficients [ n,8 ] 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="/A022215/b022215.txt">Table of n, a(n) for n = 8..190</a>
%F G.f.: x^8/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)*(1-15625*x)*(1-78125*x)*(1-390625*x)). - _Vincenzo Librandi_, Aug 10 2016
%F a(n) = Product_{i=1..8} (5^(n-i+1)-1)/(5^i-1), by definition. - _Vincenzo Librandi_, Aug 10 2016
%t Table[QBinomial[n, 8, 5], {n, 8, 20}] (* _Vincenzo Librandi_, Aug 10 2016 *)
%o (Sage) [gaussian_binomial(n,8,5) for n in range(8,17)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=8; 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=8; q=5; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 08 2018
%K nonn,easy
%O 8,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 10 2016