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Gaussian binomial coefficients [ n,2 ] for q = 8.
2

%I #20 Jul 02 2023 14:00:04

%S 1,73,4745,304265,19477641,1246606473,79783113865,5106121684105,

%T 326791806956681,20914675798619273,1338539252338766985,

%U 85666512159498155145,5482656778286418474121,350890033810959074702473

%N Gaussian binomial coefficients [ n,2 ] for q = 8.

%H Vincenzo Librandi, <a href="/A022242/b022242.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 (73, -584, 512).

%F G.f.: x^2/[(1-x)(1-8x)(1-64x)].

%F a(n) = Product_{i=1..2} (8^(n-i+1)-1)/(8^i-1), by definition. - _Vincenzo Librandi_, Aug 05 2016

%t CoefficientList[Series[1/((1-x)(1-8x)(1-64x)), {x,0,25}],x] (* _Harvey P. Dale_, Mar 13 2011 *)

%t Table[QBinomial[n, 2, 8], {n, 2, 20}] (* _Vincenzo Librandi_, Aug 05 2016 *)

%o (Sage) [gaussian_binomial(n,2,8) for n in range(2,16)] # _Zerinvary Lajos_, May 28 2009

%o (Magma) r:=2; q:=8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 05 2016

%K nonn

%O 2,2

%A _N. J. A. Sloane_.

%E Offset changed by _Vincenzo Librandi_, Aug 05 2016