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A015375
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Gaussian binomial coefficient [ n,9 ] for q=-3.
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13
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1, -14762, 326882347, -6204226946060, 123644349019377043, -2423717068608654822146, 47771556642163840723529281, -939857780045414554730512966640, 18502040831058043147238631145734166, -364157167636884405223950738210339855212
(list;
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refs;
listen;
history;
text;
internal format)
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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(((-3)^(n-i+1)-1)/((-3)^i-1), i=1..9) (by definition). - Vincenzo Librandi, Nov 04 2012
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MATHEMATICA
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Table[QBinomial[n, 9, -3], {n, 9, 20}] (* Vincenzo Librandi, Nov 04 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 9, -3) for n in xrange(9, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2009]
(MAGMA) r:=9; q:=-3; [&*[(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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Cf. Gaussian binomial coefficients [n,9] for q=-2,...,-13: A015371, A015376, A015377, A015378, A015379, A015380, A015381, A015382, A015383, A015384, A015385. - Vincenzo Librandi, Nov 04 2012
Sequence in context: A178588 A089315 A202314 * A043648 A035919 A186790
Adjacent sequences: A015372 A015373 A015374 * A015376 A015377 A015378
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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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