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A022204 Gaussian binomial coefficients [ n,5 ] for q = 4. 1

%I

%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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Last modified August 4 13:04 EDT 2020. Contains 336201 sequences. (Running on oeis4.)