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A015363
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Gaussian binomial coefficient [ n,8 ] for q=-7.
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13
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1, 5044201, 29684623509101, 170628488227082949701, 984049129188697468764456303, 5672509895284807570626050787828903, 32701168672146988445875611556849499108603, 188515500954498588979354521825234382842445990403
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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..100
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FORMULA
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a(n) = Product_{i=1..8} ((-7)^(n-i+1)-1)/((-7)^i-1). - M. F. Hasler, Nov 03 2012
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MATHEMATICA
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QBinomial[Range[8, 20], 8, -7] (* Harvey P. Dale, May 09 2012 *)
Table[QBinomial[n, 8, -7], {n, 8, 19}] (* Vincenzo Librandi, Nov 03 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 8, -7) for n in range(8, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=-7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
(PARI) A015363(n, r=8, q=-7)=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, A015360, A015361, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012
Sequence in context: A227155 A106785 A034607 * A234785 A206136 A186624
Adjacent sequences: A015360 A015361 A015362 * A015364 A015365 A015366
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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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