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Gaussian binomial coefficients [n,7] for q = 2.
3

%I #29 Sep 08 2022 08:44:46

%S 1,255,43435,6347715,866251507,114429029715,14877590196755,

%T 1919209135381395,246614610741341843,31627961868755063955,

%U 4052305562169692070035,518946525150879134496915,66441249531569955747981459

%N Gaussian binomial coefficients [n,7] for q = 2.

%H Vincenzo Librandi, <a href="/A022190/b022190.txt">Table of n, a(n) for n = 7..200</a>

%F G.f.: x^7/((1-x)*(1-2*x)*(1-4*x)*(1-8*x)*(1-16*x)*(1-32*x)*(1-64*x)*(1-128*x)). - _Vincenzo Librandi_, Aug 07 2016

%F a(n) = Product_{i=1..7} (2^(n-i+1)-1)/(2^i-1), by definition. - _Vincenzo Librandi_, Aug 02 2016

%t Table[QBinomial[n, 7, 2], {n, 7, 24}] (* _Vincenzo Librandi_, Aug 02 2016 *)

%o (Sage) [gaussian_binomial(n,7,2) for n in range(7,20)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=7; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 02 2016

%o (PARI) r=7; q=2; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, May 30 2018

%K nonn,easy

%O 7,2

%A _N. J. A. Sloane_, Jun 14 1998

%E Changed offset by _Vincenzo Librandi_, Aug 02 2016