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A022196 Gaussian binomial coefficients [ n,5 ] for q = 3. 1

%I

%S 1,364,99463,25095280,6174066262,1506472167928,366573514642546,

%T 89117945389585840,21658948312410865183,5263390747480701708292,

%U 1279025522911365763892449,310804949350361548416923680,75525744222315755534269847164

%N Gaussian binomial coefficients [ n,5 ] for q = 3.

%H Vincenzo Librandi, <a href="/A022196/b022196.txt">Table of n, a(n) for n = 5..200</a>

%F G.f.: x^5/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)). - _Vincenzo Librandi_, Aug 07 2016

%F a(n) = Product_{i=1..5} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 06 2016

%t Table[QBinomial[n, 5, 3], {n, 5, 20}] (* _Vincenzo Librandi_, Aug 07 2016 *)

%o (Sage) [gaussian_binomial(n,5,3) for n in xrange(5,17)] # _Zerinvary Lajos_, May 25 2009

%o (MAGMA) r:=5; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 07 2016

%o (PARI) r=5; q=3; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, May 30 2018

%K nonn,easy

%O 5,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 07 2016

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Last modified April 24 16:26 EDT 2019. Contains 322430 sequences. (Running on oeis4.)