login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A015410
Gaussian binomial coefficient [ n,11 ] for q=-6.
2
1, -310968905, 116041991914472611, -41905685236388916561230885, 15214999201976941569510489219969931, -5519247137793116688209551072778853951561365, 2002409531513525089470147425061900304433199288073771
OFFSET
11,2
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
FORMULA
a(n) = Product_{i=1..11} ((-6)^(n-i+1)-1)/((-6)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012
MATHEMATICA
Table[QBinomial[n, 11, -6], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)
PROG
(Sage) [gaussian_binomial(n, 11, -6) for n in range(11, 17)] # Zerinvary Lajos, May 28 2009
(Magma) r:=11; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012
CROSSREFS
Sequence in context: A251807 A184671 A034610 * A189055 A221985 A219784
KEYWORD
sign,easy
STATUS
approved