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A015360
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Gaussian binomial coefficient [ n,8 ] for q=-5.
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13
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1, 325521, 132454820421, 51329529054158421, 20082729571968536374671, 7842306707330337276457324671, 3063597127265150338968694860387171, 1196702310087594273181943625299134137171, 467463036580276600555969910576099571466559046
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OFFSET
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8,2
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REFERENCES
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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.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 8..190
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FORMULA
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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
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MATHEMATICA
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Table[QBinomial[n, 8, -5], {n, 8, 20}] (* Vincenzo Librandi, Nov 03 2012 *)
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PROG
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(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
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CROSSREFS
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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
Adjacent sequences: A015357 A015358 A015359 * A015361 A015362 A015363
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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