A015388 - OEIS

%I #23 Sep 08 2022 08:44:39

%S 1,44287,2941985410,167517069529030,10015359787639069513,

%T 588973263031690760850991,34826053765400471578213696840,

%U 2055503791013087031667210071738520,121393945396362834176064326157233601646

%N Gaussian binomial coefficient [ n,10 ] for q=-3.

%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="/A015388/b015388.txt">Table of n, a(n) for n = 10..200</a>

%F a(n) = Product_{i=1..10} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - _Vincenzo Librandi_, Nov 04 2012

%t Table[QBinomial[n, 10, -3], {n, 10, 20}] (* _Vincenzo Librandi_, Nov 04 2012 *)

%o (Sage) [gaussian_binomial(n,10,-3) for n in range(10,18)] # _Zerinvary Lajos_, May 25 2009

%o (Magma) r:=10; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // _Vincenzo Librandi_, Nov 04 2012

%Y Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015401, A015402.

%K nonn,easy

%O 10,2

%A _Olivier Gérard_