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A015371
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Gaussian binomial coefficient [ n,9 ] for q=-2.
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14
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1, -341, 232903, -105970865, 57881286463, -28735427761313, 14946527496991519, -7593183562134412385, 3902985682508407194271, -1994425683761796076272481, 1022146087305755916943130783, -523082886040328458081329117025
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OFFSET
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9,2
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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 = 9..200
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FORMULA
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a(n)=product_{i=1..9} ((-2)^(n-i+1)-1)/((-2)^i-1). - Vincenzo Librandi, Nov 04 2012
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MATHEMATICA
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Table[QBinomial[n, 9, -2], {n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 9, -2) for n in xrange(9, 21)] # [From Zerinvary Lajos, May 25 2009]
(MAGMA) r:=9; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 04 2012
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CROSSREFS
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Diagonal k=9 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012
Cf. Gaussian binomial coefficients [n,9] for q=-2,...,-13: A015375, A015376, A015377, A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012
Sequence in context: A069309 A086806 A006107 * A163582 A239271 A204751
Adjacent sequences: A015368 A015369 A015370 * A015372 A015373 A015374
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KEYWORD
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sign,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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