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A015276 Gaussian binomial coefficient [ n,3 ] for q = -8. 2
1, -455, 236665, -120935815, 61934287481, -31709385606535, 16235267484138105, -8312452980450674055, 4255976180162154314361, -2179059787976052939572615, 1115678612484825190455949945, -571227449525600988055816521095 (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
FORMULA
G.f.: x^3/((1-x)*(1+8*x)*(1-64*x)*(1+512*x)). - Bruno Berselli, Oct 30 2012
a(n) = (-1 + 57*8^(2n-3) + (-1)^n*8^(n-2)*(57-8^(2n-1)))/290871. - Bruno Berselli, Oct 30 2012
a(n) = Product_{i=1..3} ((-8)^(n-i+1)-1)/((-8)^i-1) (by definition). - Vincenzo Librandi, Aug 02 2016
MATHEMATICA
Table[QBinomial[n, 3, -8], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
PROG
(Sage) [gaussian_binomial(n, 3, -8) for n in range(3, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=-8; [&*[(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: A251337 A282232 A061544 * A145528 A203058 A116331
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved

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Last modified April 16 17:08 EDT 2024. Contains 371749 sequences. (Running on oeis4.)