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A015424
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Gaussian binomial coefficient [ n,12 ] for q=-3.
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2
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1, 398581, 238300021051, 122119467087816511, 65710531328480659504924, 34778150788062009177434607244, 18507923283033747485964552371646724, 9831373896055842251635498188040677794164
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OFFSET
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12,2
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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 = 12..180
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FORMULA
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a(n) = Product_{i=1..12} ((-3)^(n-i+1)-1)/((-3)^i-1) (by definition). - Vincenzo Librandi, Nov 06 2012
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MATHEMATICA
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QBinomial[Range[12, 20], 12, -3] (* Harvey P. Dale, Dec 18 2011 *)
Table[QBinomial[n, 12, -3], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 12, -3) for n in range(12, 20)] # Zerinvary Lajos, May 28 2009
(MAGMA) r:=12; q:=-3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 06 2012
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CROSSREFS
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Sequence in context: A250925 A230148 A209784 * A083634 A209910 A190837
Adjacent sequences: A015421 A015422 A015423 * A015425 A015426 A015427
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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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