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A022202 Gaussian binomial coefficients [ n,11 ] for q = 3. 1

%I

%S 1,265720,52955405230,9741692640081640,1747282899667791058573,

%T 310804949350361548416923680,55133793282290501540016988429720,

%U 9771253933538933149312961201158497760,1731212183148357775944585240618840930624286

%N Gaussian binomial coefficients [ n,11 ] 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="/A022202/b022202.txt">Table of n, a(n) for n = 11..200</a>

%F G.f.: x^11/((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)*(1-177147*x)). - _Vincenzo Librandi_, Aug 11 2016

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

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

%o (Sage) [gaussian_binomial(n,11,3) for n in xrange(11,20)] # _Zerinvary Lajos_, May 28 2009

%o (MAGMA) r:=11; 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=11; 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 11,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 11 2016

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Last modified April 26 04:37 EDT 2019. Contains 322469 sequences. (Running on oeis4.)