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A015279 Gaussian binomial coefficient [ n,3 ] for q = -11. 2
1, -1220, 1637362, -2177691460, 2898705467483, -3858153003126520, 5135204548028317764, -6834956902420811530200, 9097327679593690752247605, -12108543136400139930131294300, 16116470915170412804822871108406 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
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
Index entries for linear recurrences with constant coefficients, signature (-1220,148962,1623820,-1771561).
FORMULA
a(n) = product(((-11)^(n-i+1)-1)/((-11)^i-1), i=1..3) (by definition). - Vincenzo Librandi, Aug 02 2016
G.f.: x^3 / ( (x-1)*(11*x+1)*(121*x-1)*(1331*x+1) ). - R. J. Mathar, Aug 03 2016
MATHEMATICA
Table[QBinomial[n, 3, -11], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
PROG
(Sage) [gaussian_binomial(n, 3, -11) for n in range(3, 14)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016
CROSSREFS
Sequence in context: A031781 A069400 A233660 * A179140 A091790 A053655
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved

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Last modified July 13 09:13 EDT 2024. Contains 374274 sequences. (Running on oeis4.)