A015405 - OEIS

%I #17 Sep 08 2022 08:44:39

%S 1,-1365,3727815,-6785865905,14824402656063,-29439916001972385,

%T 61250446192484546335,-124468028808034701006945,

%U 255910660218571393553843871,-523082886040328458081329117025

%N Gaussian binomial coefficient [ n,11 ] for q=-2.

%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="/A015405/b015405.txt">Table of n, a(n) for n = 11..200</a>

%H <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries related to Gaussian binomial coefficients</a>.

%F a(n) = Product_{i=1..11} ((-2)^(n-i+1)-1)/((-2)^i-1). - _Vincenzo Librandi_, Nov 05 2012

%t Table[QBinomial[n, 11, -2], {n, 11, 20}] (* _Vincenzo Librandi_, Nov 05 2012 *)

%o (Sage) [gaussian_binomial(n,11,-2) for n in range(11,21)] # _Zerinvary Lajos_, May 28 2009

%o (Magma) r:=11; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 05 2012

%Y Diagonal k=11 of the triangular array A015109. See there for further references and programs. - _M. F. Hasler_, Nov 04 2012

%K sign,easy

%O 11,2

%A _Olivier Gérard_