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%I #17 Sep 08 2022 08:44:46
%S 1,21845,381767589,6354157930725,104514759495347685,
%T 1714043588198181437925,28089747579101385828291045,
%U 460250514083576206796548772325,7540859480106603961931048583270885,123549912998815788062283863044996567525
%N Gaussian binomial coefficients [ n,7 ] for q = 4.
%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="/A022206/b022206.txt">Table of n, a(n) for n = 7..200</a>
%F G.f.: x^7/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)). - _Vincenzo Librandi_, Aug 11 2016
%F a(n) = Product_{i=1..7} (4^(n-i+1)-1)/(4^i-1), by definition. - _Vincenzo Librandi_, Aug 11 2016
%t Table[QBinomial[n, 7, 4], {n, 7, 20}] (* _Vincenzo Librandi_, Aug 11 2016 *)
%o (Sage) [gaussian_binomial(n,7,4) for n in range(7,17)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=7; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 11 2016
%o (PARI) r=7; q=4; 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 7,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 11 2016
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