OFFSET
8,2
REFERENCES
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.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 8..100
FORMULA
a(n) = Product_{i=1..8} ((-12)^(n-i+1)-1)/((-12)^i-1). - M. F. Hasler, Nov 03 2012
MAPLE
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
MATHEMATICA
Table[QBinomial[n, 8, -12], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)
PROG
(Sage) [gaussian_binomial(n, 8, -12) for n in range(8, 14)] # Zerinvary Lajos, May 24 2009
(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
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved