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

%S 1,400,140050,48177200,16531644851,5670690600800,1945063360640100,

%T 667157540444234400,228835075951868449701,78490432990886231801200,

%U 26922218610904350161500150,9234320988196680367732171600

%N Gaussian binomial coefficients [ n,3 ] for q = 7.

%H Vincenzo Librandi, <a href="/A022232/b022232.txt">Table of n, a(n) for n = 3..200</a>

%F G.f.: x^3/((1-x)*(1-7*x)*(1-49*x)*(1-343*x)).

%F a(n) = Product_{i=1..3} (7^(n-i+1)-1)/(7^i-1), by definition. - _Vincenzo Librandi_, Aug 06 2016

%t Table[QBinomial[n, 3, 7], {n, 3, 20}] (* _Vincenzo Librandi_, Aug 06 2016 *)

%o (Sage) [gaussian_binomial(n,3,7) for n in range(3,15)] # _Zerinvary Lajos_, May 27 2009

%o (Magma) r:=3; 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=3; 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,easy

%O 3,2

%A _N. J. A. Sloane_

%E Offset changed by _Vincenzo Librandi_, Aug 06 2016