cp's OEIS Frontend

A022199 Gaussian binomial coefficients [ n,8 ] for q = 3.

%I A022199 #17 Sep 08 2022 08:44:46
%S A022199 1,9841,72636421,494894285941,3287582741506063,21658948312410865183,
%T A022199 142299528422960399756323,934054234760012359481199283,
%U A022199 6129263888495201102915629695046,40216143252770054194345243936096486,263862583736385343242102717216527933566
%N A022199 Gaussian binomial coefficients [ n,8 ] for q = 3.
%D A022199 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022199 Vincenzo Librandi, <a href="/A022199/b022199.txt">Table of n, a(n) for n = 8..200</a>
%F A022199 G.f.: x^8/((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)). - _Vincenzo Librandi_, Aug 07 2016
%F A022199 a(n) = Product_{i=1..8} (3^(n-i+1)-1)/(3^i-1), by definition. - _Vincenzo Librandi_, Aug 07 2016
%t A022199 Table[QBinomial[n, 8, 3], {n, 8, 20}] (* _Vincenzo Librandi_, Aug 07 2016 *)
%o A022199 (Sage) [gaussian_binomial(n,8,3) for n in range(8,19)] # _Zerinvary Lajos_, May 25 2009
%o A022199 (Magma) r:=8; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 07 2016
%o A022199 (PARI) r=8; 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 A022199 nonn,easy
%O A022199 8,2
%A A022199 _N. J. A. Sloane_
%E A022199 Offset changed by _Vincenzo Librandi_, Aug 07 2016