|
%I #21 Sep 08 2022 08:44:40
%S 1,203450521,51740143068101671,12531617923263572089314671,
%T 3064380040090865325461356053952796,
%U 747900330120650910670378436164144443652796,182604540723920504029015495725080327984747417027796,44580616068292567497216163076570130750072904955316534527796
%N Gaussian binomial coefficient [ n,12 ] for q=-5.
%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="/A015427/b015427.txt">Table of n, a(n) for n = 12..130</a>
%F a(n) = Product_{i=1..12} ((-5)^(n-i+1)-1)/((-5)^i-1). - _Vincenzo Librandi_, Nov 06 2012
%t QBinomial[Range[12,20],12,-5] (* _Harvey P. Dale_, Mar 28 2012 *)
%t Table[QBinomial[n, 12, -5], {n, 12, 20}] (* _Vincenzo Librandi_, Nov 06 2012 *)
%o (Sage) [gaussian_binomial(n,12,-5) for n in range(12,18)] # _Zerinvary Lajos_, May 28 2009
%o (Magma) r:=12; q:=-5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // _Vincenzo Librandi_, Nov 06 2012
%K nonn,easy
%O 12,2
%A _Olivier Gérard_
%E More terms from _Harvey P. Dale_, Mar 28 2012
|
