%I #24 Sep 08 2022 08:44:46
%S 1,6725601,39579496050501,228835075951868449701,
%T 1319738336534843578720956303,7608481579300344488889504665693103,
%U 43861755035533826577243997768793428552803,252854596323205247053675081227392663237129990403
%N Gaussian binomial coefficients [ n,8 ] for q = 7.
%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="/A022237/b022237.txt">Table of n, a(n) for n = 8..150</a>
%F a(n) = Product_{i=1..8} (7^(n-i+1)-1)/(7^i-1), by definition. - _Vincenzo Librandi_, Aug 06 2016
%F G.f.: x^8/((1 - x)*(1 - 7*x)*(1 - 49*x)*(1 - 343*x)*(1 - 2401*x)*(1 - 16807*x)*(1 - 117649*x)*(1 - 823543*x)*(1 - 5764801*x)). - _Ilya Gutkovskiy_, Aug 06 2016
%t Drop[QBinomial[Range[0,20],8,7],8] (* _Harvey P. Dale_, Mar 26 2013 *)
%o (Sage) [gaussian_binomial(n,8,7) for n in range(8,15)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=8; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 06 2016
%K nonn,easy
%O 8,2
%A _N. J. A. Sloane_.
%E One additional term, offset corrected, _Harvey P. Dale_, Mar 26 2013