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Gaussian binomial coefficients [ n,2 ] for q = 9.
1

%I #17 Jul 02 2023 14:01:11

%S 1,91,7462,605242,49031983,3971657053,321704819164,26058095733124,

%T 2110705802810605,170967170463507055,13848340811466703906,

%U 1121715605764106708446,90858964067210376612667,7359576089446900104682897

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

%H Vincenzo Librandi, <a href="/A022253/b022253.txt">Table of n, a(n) for n = 2..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (91, -819, 729).

%F G.f.: 1/[(1-x)(1-9x)(1-81x)].

%F a(n) = Product_{i=1..2} (9^(n-i+1)-1)/(9^i-1), by definition. - _Vincenzo Librandi_, Aug 04 2016

%t Table[QBinomial[n, 2, 9], {n, 2, 20}] (* _Vincenzo Librandi_, Aug 04 2016 *)

%o (Sage) [gaussian_binomial(n,2,9) for n in range(2,16)] # _Zerinvary Lajos_, May 28 2009

%o (Magma) r:=2; 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 2,2

%A _N. J. A. Sloane_.

%E Offset changed by _Vincenzo Librandi_, Aug 04 2016