A022203 - OEIS

%I #16 Sep 08 2022 08:44:46

%S 1,797161,476599444231,263026177881648511,141530177899268957392924,

%T 75525744222315755534269847164,40192610828533997938427918835113044,

%U 21369772545260475331545384574852469714164,11358504503408920628447755309084790198295654610

%N Gaussian binomial coefficients [ n,12 ] 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="/A022203/b022203.txt">Table of n, a(n) for n = 12..180</a>

%F G.f.: x^12/((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)*(1-531441*x) ). - _Vincenzo Librandi_, Aug 11 2016

%F a(n) = Product_{i=1..12} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 11 2016

%t Table[QBinomial[n, 12, 3], {n, 12, 20}] (* _Vincenzo Librandi_, Aug 11 2016 *)

%o (Sage) [gaussian_binomial(n,12,3) for n in range(12,21)] # _Zerinvary Lajos_, May 28 2009

%o (Magma) r:=12; 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=12; q=3; for(n=r,35, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 01 2018

%K nonn,easy

%O 12,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 11 2016