%I #23 Sep 08 2022 08:44:39
%S 1,57154490053,3563602618051323347605,
%T 220521264778812882986788501660885,
%U 13654753975171772337501943609360145428875733,845462977543736084817433183822531039414960234418458069
%N Gaussian binomial coefficient [ n,10 ] for q=-12.
%D J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H Vincenzo Librandi, <a href="/A015401/b015401.txt">Table of n, a(n) for n = 10..100</a>
%F a(n) = Product_{i=1..10} ((-12)^(n-i+1)-1)/((-12)^i-1) (by definition). - _Vincenzo Librandi_, Nov 05 2012
%t Table[QBinomial[n, 10, -12], {n, 10, 20}] (* _Vincenzo Librandi_, Nov 05 2012 *)
%o (Sage) [gaussian_binomial(n,10,-12) for n in range(10,15)] # _Zerinvary Lajos_, May 25 2009
%o (Magma) r:=10; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 04 2012
%Y Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015402.
%K nonn,easy
%O 10,2
%A _Olivier GĂ©rard_