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%I #17 Sep 08 2022 08:44:46
%S 1,5461,23859109,99277752549,408235958349285,1673768626404966885,
%T 6857430062381149327845,28089747579101385828291045,
%U 115057361291389776393497498085,471276749188750005563056686387685,1930351405154232225472089767795511781
%N Gaussian binomial coefficients [ n,6 ] 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="/A022205/b022205.txt">Table of n, a(n) for n = 6..200</a>
%F G.f.: x^6/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)). - _Vincenzo Librandi_, Aug 11 2016
%F a(n) = Product_{i=1..6} (4^(n-i+1)-1)/(4^i-1), by definition. - _Vincenzo Librandi_, Aug 11 2016
%t Table[QBinomial[n,6,4], {n,6,20}] (* _Vincenzo Librandi_, Aug 11 2016 *)
%o (Sage) [gaussian_binomial(n,6,4) for n in range(6,17)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=6; 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=6; q=4; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 01 2018
%K nonn,easy
%O 6,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 11 2016
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