|
%I #23 Sep 08 2022 08:44:46
%S 1,335923,96723701071,27202382491194295,7620806375898728694055,
%T 2133612436978999661759040967,597287733061433620469903134280071,
%U 167202936130018543413483273700960235527,46806148995565935663430369990805328306755335
%N Gaussian binomial coefficients [ n,7 ] for q = 6.
%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="/A022225/b022225.txt">Table of n, a(n) for n = 7..190</a>
%F G.f.: x^7/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)*(1-7776*x)*(1-46656*x)*(1-279936*x)). - _Vincenzo Librandi_, Aug 12 2016
%F a(n) = Product_{i=1..7} (6^(n-i+1)-1)/(6^i-1), by definition. - _Vincenzo Librandi_, Aug 12 2016
%t Drop[QBinomial[Range[20],7,6],6] (* _Harvey P. Dale_, Mar 27 2012 *)
%t Table[QBinomial[n, 7, 6], {n, 7, 20}] (* _Vincenzo Librandi_, Aug 12 2016 *)
%o (Sage) [gaussian_binomial(n,7,6) for n in range(7,16)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=7; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 12 2016
%o (PARI) r=7; q=6; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ _G. C. Greubel_, Jun 13 2018
%K nonn,easy
%O 7,2
%A _N. J. A. Sloane_
|
