%I #18 Sep 08 2022 08:44:46

%S 1,19608,336416907,5670690600800,95347005938577702,

%T 1602592475815614015216,26935000671139346639437914,

%U 452697105941691435357049202400,7608481579300344488889504665693103,127875753071992714335358328311551866824

%N Gaussian binomial coefficients [ n,5 ] for q = 7.

%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="/A022234/b022234.txt">Table of n, a(n) for n = 5..200</a>

%F a(n) = Product_{i=1..5} (7^(n-i+1)-1)/(7^i-1), by definition. - _Vincenzo Librandi_, Aug 06 2016

%F G.f.: x^5/((1 - x)*(1 - 7*x)*(1 - 49*x)*(1 - 343*x)*(1 - 2401*x)*(1 - 16807*x)). - _Ilya Gutkovskiy_, Aug 06 2016

%t Table[QBinomial[n, 5, 7], {n, 5, 20}] (* _Vincenzo Librandi_, Aug 06 2016 *)

%o (Sage) [gaussian_binomial(n,5,7) for n in range(5,15)] # _Zerinvary Lajos_, May 27 2009

%o (Magma) r:=5; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Aug 06 2016

%o (PARI) r=5; q=7; 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

%O 5,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 06 2016