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%I #22 Jul 02 2023 13:57:45
%S 1,43,1591,57535,2072815,74630671,2686760143,96723701071,
%T 3482055254095,125354001240655,4512744117222991,162458788655384143,
%U 5848516394205967951,210546590207087679055,7579677247549193442895,272868380912335185925711
%N Gaussian binomial coefficients [ n,2 ] for q = 6.
%H Vincenzo Librandi, <a href="/A022220/b022220.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 (43, -258, 216).
%F G.f.: x^2/((1-x)*(1-6*x)*(1-36*x)).
%F a(n) = Product_{i=1..2} (6^(n-i+1)-1)/(6^i-1), by definition. - _Vincenzo Librandi_, Aug 16 2016
%t Table[QBinomial[n, 2, 6], {n, 2, 20}] (* _Vincenzo Librandi_, Aug 10 2016 *)
%o (Sage) [gaussian_binomial(n,2,6) for n in range(2,17)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=2; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 10 2016
%o (PARI) r=2; q=6; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 07 2018
%K nonn,easy
%O 2,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 10 2016
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