Search: id:a015386
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A015386
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Gaussian binomial coefficient [ n,10 ] for q=-2.
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+0
13
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1, 683, 932295, 848699215, 926949282623, 920460637644639, 957498220445101855, 972884994173649887135, 1000137219716325891620511, 1022146087305755916943130783, 1047699739488399814866709052575, 1072321450350081081965428740719775
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OFFSET
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10,2
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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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Index entries for linear recurrences with constant coefficients, signature (683,465806,-106203768, -14443712448,903388560384,28908433932288,-473291569496064, -3563607111499776,16004972290244608,24030926136672256,-36028797018963968).
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FORMULA
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a(n) = Product_{i=1..10} ((-2)^(n-i+1)-1)/((-2)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012
G.f.: x^10 / ( (x-1)*(512*x+1)*(64*x-1)*(128*x+1)*(1024*x-1)*(2*x+1)*(8*x+1)*(32*x+1)*(16*x-1)*(4*x-1)*(256*x-1) ). - R. J. Mathar, Sep 22 2016
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MATHEMATICA
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PROG
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(Sage) [gaussian_binomial(n, 10, -2) for n in range(10, 21)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 04 2012
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CROSSREFS
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Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015388, A015390, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015401, A015402.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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