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Gaussian binomial coefficients [ n,3 ] for q = 9.
1

%I #14 Sep 08 2022 08:44:46

%S 1,820,605242,441826660,322140667123,234844517989720,

%T 171201975319325044,124806266065883690200,90983770072735012966405,

%U 66327168553990994916016300,48352505889707776105242586606,35248976794718684386485952344220

%N Gaussian binomial coefficients [ n,3 ] for q = 9.

%H Vincenzo Librandi, <a href="/A022254/b022254.txt">Table of n, a(n) for n = 3..200</a>

%F a(n) = Product_{i=1..3} (9^(n-i+1)-1)/(9^i-1), by definition. - _Vincenzo Librandi_, Aug 04 2016

%t Table[QBinomial[n, 3, 9], {n, 3, 20}] (* _Vincenzo Librandi_, Aug 04 2016 *)

%o (Sage) [gaussian_binomial(n,3,9) for n in range(3,15)] # _Zerinvary Lajos_, May 27 2009

%o (Magma) r:=3; q:=9; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 04 2016

%K nonn

%O 3,2

%A _N. J. A. Sloane_.

%E Offset changed by _Vincenzo Librandi_, Aug 04 2016