%I #17 Sep 08 2022 08:44:46
%S 1,1398101,1563749404581,1665737215212030181,
%T 1753501675591663698472421,1840477112202685809580351554021,
%U 1930351405154232225472089767795511781,2024243704924003025844684284218991557841381
%N Gaussian binomial coefficients [ n,10 ] for q = 4.
%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="/A022209/b022209.txt">Table of n, a(n) for n = 10..170</a>
%F G.f.: x^10/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)*(1-65536*x)*(1-262144*x)*(1-1048576*x)). - _Vincenzo Librandi_, Aug 11 2016
%F a(n) = Product_{i=1..10} (4^(n-i+1)-1)/(4^i-1), by definition. - _Vincenzo Librandi_, Aug 11 2016
%t Table[QBinomial[n, 10, 4], {n, 10, 20}] (* _Vincenzo Librandi_, Aug 11 2016 *)
%o (Sage) [gaussian_binomial(n,10,4) for n in range(10,18)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=10; q:=4; [&*[(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=4; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 04 2018
%K nonn,easy
%O 10,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 11 2016