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A022201 Gaussian binomial coefficients [ n,10 ] for q = 3. 1

%I

%S 1,88573,5883904390,360801469802830,21571273555248777493,

%T 1279025522911365763892449,75628919722004322604209288760,

%U 4467854961017673003571751798888920,263862583736385343242102717216527933566

%N Gaussian binomial coefficients [ n,10 ] for q = 3.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

%H Vincenzo Librandi, <a href="/A022201/b022201.txt">Table of n, a(n) for n = 10..200</a>

%F G:f.: x^10/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)*(1-81*x)*(1-243*x)*(1-729*x)*(1-2187*x)*(1-6561*x)*(1-19683*x)*(1-59049*x)). - _Vincenzo Librandi_, Aug 11 2016

%F a(n) = Product_{i=1..10} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 11 2016

%t Table[QBinomial[n, 10, 3], {n, 10, 20}] (* _Vincenzo Librandi_, Aug 11 2016 *)

%o (Sage) [gaussian_binomial(n,10,3) for n in xrange(10,19)] # _Zerinvary Lajos_, May 25 2009

%o (MAGMA) r:=10; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 11 2016

%o (PARI) r=10; q=3; 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 10,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 11 2016

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Last modified April 25 16:08 EDT 2019. Contains 322461 sequences. (Running on oeis4.)