cp's OEIS Frontend

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

%I A022202 #17 Sep 08 2022 08:44:46
%S A022202 1,265720,52955405230,9741692640081640,1747282899667791058573,
%T A022202 310804949350361548416923680,55133793282290501540016988429720,
%U A022202 9771253933538933149312961201158497760,1731212183148357775944585240618840930624286
%N A022202 Gaussian binomial coefficients [ n,11 ] for q = 3.
%D A022202 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022202 Vincenzo Librandi, <a href="/A022202/b022202.txt">Table of n, a(n) for n = 11..200</a>
%F A022202 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 A022202 a(n) = Product_{i=1..11} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 11 2016
%t A022202 Table[QBinomial[n, 11, 3], {n, 11, 20}] (* _Vincenzo Librandi_, Aug 11 2016 *)
%o A022202 (Sage) [gaussian_binomial(n,11,3) for n in range(11,20)] # _Zerinvary Lajos_, May 28 2009
%o A022202 (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 A022202 (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 A022202 nonn,easy
%O A022202 11,2
%A A022202 _N. J. A. Sloane_
%E A022202 Offset changed by _Vincenzo Librandi_, Aug 11 2016