|
%I #20 Sep 08 2022 08:44:46
%S 1,87381,6108368805,406672215935205,26756185103024942565,
%T 1755207390500040817377765,115057361291389776393497498085,
%U 7540859480106603961931048583270885,494205307747746503853075131001823990245
%N Gaussian binomial coefficients [ n,8 ] 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="/A022207/b022207.txt">Table of n, a(n) for n = 8..200</a>
%F G.f.: x^8/((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)). - _Vincenzo Librandi_, Aug 11 2016
%F a(n) = Product_{i=1..8} (4^(n-i+1)-1)/(4^i-1), by definition. - _Vincenzo Librandi_, Aug 11 2016
%t QBinomial[Range[8,20],8,4] (* _Harvey P. Dale_, Jan 27 2012 *)
%t Table[QBinomial[n, 8, 4], {n, 8, 20}] (* _Vincenzo Librandi_, Aug 11 2016 *)
%o (Sage) [gaussian_binomial(n,8,4) for n in range(8,17)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=8; 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=8; 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 8,2
%A _N. J. A. Sloane_
%E Offset changed by _Vincenzo Librandi_, Aug 11 2016
|
