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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

Vincenzo Librandi, Table of n, a(n) for n = 3..200

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

Adjacent sequences:  A015276 A015277 A015278 * A015280 A015281 A015282

KEYWORD

sign,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)