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A015431
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Gaussian binomial coefficient [ n,12 ] for q=-8.
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2
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1, 61083979321, 4264288605349394427001, 292468454161371994489927453227641, 20103187136428193301141459556344509715532409, 1381438342588687480407961010312719764427906885156653689, 94932082182896025238148883982319050364413593497347296287825382009
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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..100
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FORMULA
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a(n) = product(((-8)^(n-i+1)-1)/((-8)^i-1), i=1..12) (by definition). - Vincenzo Librandi, Nov 06 2012
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MATHEMATICA
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Table[QBinomial[n, 12, -8], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 12, -8) for n in xrange(12, 17)] # [From Zerinvary Lajos, May 28 2009]
(MAGMA) r:=12; q:=-8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012
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CROSSREFS
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Sequence in context: A015401 A196753 A258424 * A017410 A017530 A216020
Adjacent sequences: A015428 A015429 A015430 * A015432 A015433 A015434
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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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