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%I #16 Sep 08 2022 08:44:46
%S 1,1365,1490853,1550842085,1594283908581,1634141006295525,
%T 1673768626404966885,1714043588198181437925,1755207390500040817377765,
%U 1797339217481455290934231525,1840477112202685809580351554021
%N Gaussian binomial coefficients [ n,5 ] for q = 4.
%H Vincenzo Librandi, <a href="/A022204/b022204.txt">Table of n, a(n) for n = 5..200</a>
%F G.f.: x^5/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)). - _Vincenzo Librandi_, Aug 11 2016
%F a(n) = Product_{i=1..5} (4^(n-i+1)-1)/(4^i-1), by definition. - _Vincenzo Librandi_, Aug 11 2016
%t Table[QBinomial[n, 5, 4], {n, 5, 20}] (* _Vincenzo Librandi_, Aug 11 2016 *)
%o (Sage) [gaussian_binomial(n,5,4) for n in range(5,16)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=5; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 11 2016
%o (PARI) r=5; q=4; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 01 2018
%K nonn,easy
%O 5,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 11 2016
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