%I #23 Sep 08 2022 08:44:46

%S 1,1023,698027,408345795,222984027123,117843461817939,

%T 61291693863308051,31627961868755063955,16256896431763117598611,

%U 8339787869494479328087443,4274137206973266943778085267,2189425218271613769209626653075

%N Gaussian binomial coefficients [ n,9 ] for q = 2.

%H Vincenzo Librandi, <a href="/A022192/b022192.txt">Table of n, a(n) for n = 9..200</a>

%F a(n) = Product_{i=1..9} (2^(n-i+1)-1)/(2^i-1), by definition. - _Vincenzo Librandi_, Aug 02 2016

%F G.f.: x^9/Product_{0<=i<=9} (1-2^i*x). - _Robert Israel_, Apr 23 2017

%p seq(eval(expand(QDifferenceEquations:-QBinomial(n,9,q)),q=2),n=9..50);

%t QBinomial[Range[9,20],9,2] (* _Harvey P. Dale_, Jul 24 2016 *)

%o (Sage) [gaussian_binomial(n,9,2) for n in range(9,21)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=9; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 03 2016

%o (PARI) r=9; 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

%O 9,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 03 2016