%I #23 Sep 08 2022 08:44:39
%S 1,396906181,171855836163195541,73852125402551558141191381,
%T 31756593605318274408653251348629973,
%U 13654699102424414895934644240803700147539413,5871272644707452307243912611380074655778555267227093
%N Gaussian binomial coefficient [ n,8 ] 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="/A015369/b015369.txt">Table of n, a(n) for n = 8..100</a>
%F a(n) = Product_{i=1..8} ((-12)^(n-i+1)-1)/((-12)^i-1). - _M. F. Hasler_, Nov 03 2012
%p A015369:=n->mul(((-12)^(n-i+1)-1)/((-12)^i-1), i=1..8): seq(A015369(n), n=8..20); # _Wesley Ivan Hurt_, Jan 29 2017
%t Table[QBinomial[n, 8, -12], {n, 8, 14}] (* _Vincenzo Librandi_, Nov 03 2012 *)
%o (Sage) [gaussian_binomial(n,8,-12) for n in range(8,14)] # _Zerinvary Lajos_, May 24 2009
%o (Magma) r:=8; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // _Vincenzo Librandi_, Nov 03 2012
%o (PARI) A015369(n,r=8,q=-12)=prod(i=1,r,(q^(n-i+1)-1)/(q^i-1)) \\ _M. F. Hasler_, Nov 03 2012
%Y Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015370. - _M. F. Hasler_, Nov 03 2012
%K nonn,easy
%O 8,2
%A _Olivier GĂ©rard_