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A015275 Gaussian binomial coefficient [ n,3 ] for q = -7. 2
1, -300, 105050, -35927100, 12328144851, -4228301370600, 1450319733570100, -497459062806004200, 170628488227082949701, -58525570007342935110900, 20074270583791406305395150, -6885474806748086165925231300 (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+7*x)*(1-49*x)*(1+343*x)). - Bruno Berselli, Oct 30 2012
a(n) = (-1 + 43*7^(2n-3) + (-1)^n*7^(n-2)*(43-7^(2n-1)))/132096. - Bruno Berselli, Oct 30 2012
MATHEMATICA
QBinomial[Range[3, 20], 3, -7] (* Harvey P. Dale, Apr 09 2012 *)
Table[QBinomial[n, 3, -7], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
PROG
(Sage) [gaussian_binomial(n, 3, -7) for n in range(3, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=3; q:=-7; [&*[(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: A190880 A063935 A294687 * A051306 A151609 A004225
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved

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Last modified May 29 20:11 EDT 2024. Contains 372952 sequences. (Running on oeis4.)