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A015344 Gaussian binomial coefficient [ n,7 ] for q = -5. 2
1, -65104, 5298179796, -410635172794704, 32132285187903171546, -2509531719872244898534704, 196069714237340352552410777796, -15317750355077977702804539604534704, 1196702310087594273181943625299134137171 (list; graph; refs; listen; history; text; internal format)
OFFSET
7,2
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 (-65104,1059648980,3284911838000,-2057018110093750,-256633737343750000,6467584106445312500,31044006347656250000,-37252902984619140625).
FORMULA
G.f.: x^7 / ( (x-1)*(5*x+1)*(25*x-1)*(625*x-1)*(78125*x+1)*(125*x+1)*(15625*x-1)*(3125*x+1) ). - R. J. Mathar, Sep 02 2016
MATHEMATICA
Table[QBinomial[n, 7, -5], {n, 7, 20}] (* Vincenzo Librandi, Nov 02 2012 *)
PROG
(Sage) [gaussian_binomial(n, 7, -5) for n in range(7, 15)] # Zerinvary Lajos, May 27 2009
(Magma) r:=7; q:=-5; [&*[(1 - q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // Vincenzo Librandi, Nov 02 2012
CROSSREFS
Sequence in context: A183975 A234908 A204640 * A184148 A083608 A102277
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Dec 11 1999
STATUS
approved

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Last modified March 28 07:46 EDT 2024. Contains 371235 sequences. (Running on oeis4.)