|
%I #27 Sep 08 2022 08:44:46
%S 1,97656,7947261556,625886840206056,48975769621072897306,
%T 3827456772141158994166056,299039198587280398947721603556,
%U 23362736428829868448189697999416056,1825218456001772231793929085435472462931
%N Gaussian binomial coefficients [ n,7 ] for q = 5.
%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="/A022214/b022214.txt">Table of n, a(n) for n = 7..200</a>
%F G.f.: x^7/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)*(1-15625*x)*(1-78125*x)). - _Vincenzo Librandi_, Aug 10 2016
%F a(n) = Product_{i=1..7} (5^(n-i+1)-1)/(5^i-1), by definition. - _Vincenzo Librandi_, Aug 10 2016
%t Table[QBinomial[n,7,5], {n, 7, 20}] (* _Harvey P. Dale_, Sep 18 2011 *)
%o (Sage) [gaussian_binomial(n,7,5) for n in range(7,16)] # _Zerinvary Lajos_, May 27 2009
%o (Magma) r:=7; q:=5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 10 2016
%o (PARI) r=7; q=5; 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 7,2
%A _N. J. A. Sloane_
|
