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A015345
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Gaussian binomial coefficient [ n,7 ] for q = -6.
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2
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1, -239945, 69088371619, -19251196169490725, 5393264335151280477835, -1509574711680960125598763925, 422593364163884169440003098013995, -118298673397216914972187267242547690325, 33116077152651051199781730118147946460139435
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OFFSET
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7,2
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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 = 7..190
Index entries for linear recurrences with constant coefficients, signature (-239945,11514768594,89124308917560,-115609163009731776,-24949102541146076160,902345215627683201024,5263661621405464657920,-6140942214464815497216)
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FORMULA
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G.f.: x^7 / ( (x-1)*(279936*x+1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1)*(46656*x-1) ). - R. J. Mathar, Sep 02 2016
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MATHEMATICA
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Table[QBinomial[n, 7, -6], {n, 7, 20}] (* Vincenzo Librandi, Nov 02 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 7, -6) for n in range(7, 15)] # Zerinvary Lajos, May 27 2009
(MAGMA) r:=7; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..15]]; // Vincenzo Librandi, Nov 02 2012
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CROSSREFS
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Sequence in context: A237396 A234547 A234709 * A187960 A190388 A249194
Adjacent sequences: A015342 A015343 A015344 * A015346 A015347 A015348
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KEYWORD
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sign,easy
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AUTHOR
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Olivier Gérard, Dec 11 1999
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STATUS
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approved
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