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%I #20 Sep 08 2022 08:44:46
%S 1,48427561,2110705802810605,90983770072735012966405,
%T 3917150001348391097251303957615,
%U 168623318873839155489174680568370759015,7258694620170400715835032365617891585605600635,312463067466939934510699888848526630609825159414503235
%N Gaussian binomial coefficients [ n,8 ] for q = 9.
%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="/A022259/b022259.txt">Table of n, a(n) for n = 8..140</a>
%F a(n) = Product_{i=1..8} (9^(n-i+1)-1)/(9^i-1), by definition. - _Vincenzo Librandi_, Aug 04 2016
%F G.f.: x^8/((1 - x)*(1 - 9*x)*(1 - 81*x)*(1 - 729*x)*(1 - 6561*x)*(1 - 59049*x)*(1 - 531441*x)*(1 - 4782969*x)*(1 - 43046721*x)). - _Ilya Gutkovskiy_, Aug 04 2016
%t QBinomial[Range[8,20],8,9] (* _Harvey P. Dale_, Jun 21 2012 *)
%t Table[QBinomial[n, 8, 9], {n, 8, 20}] (* _Vincenzo Librandi_, Aug 04 2016 *)
%o (Sage) [gaussian_binomial(n,8,9) for n in range(8,16)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=8; q:=9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 04 2016
%K nonn
%O 8,2
%A _N. J. A. Sloane_.
%E Offset corrected by _Harvey P. Dale_, Jun 21 2012
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