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A015360 Gaussian binomial coefficient [ n,8 ] for q=-5. 13
1, 325521, 132454820421, 51329529054158421, 20082729571968536374671, 7842306707330337276457324671, 3063597127265150338968694860387171, 1196702310087594273181943625299134137171, 467463036580276600555969910576099571466559046 (list; graph; refs; listen; history; text; internal format)
OFFSET
8,2
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
a(n) = Product_{i=1..8} ((-5)^(n-i+1)-1)/((-5)^i-1). - M. F. Hasler, Nov 03 2012
G.f.: -x^8 / ( (x-1)*(5*x+1)*(390625*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, 8, -5], {n, 8, 20}] (* Vincenzo Librandi, Nov 03 2012 *)
PROG
(Sage) [gaussian_binomial(n, 8, -5) for n in range(8, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=-5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
(PARI) A015360(n, r=8, q=-5)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
CROSSREFS
Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015361, A015363, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012
Sequence in context: A186836 A237223 A250910 * A209847 A237306 A210387
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)