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A015423
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Gaussian binomial coefficient [ n,12 ] for q=-2.
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2
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1, 2731, 14913991, 54301841231, 237244744338239, 942314556807454559, 3920970870875818419999, 15935828658299317547308959, 65529064844612576067331339935, 267883966717492783113707839256735
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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..200
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FORMULA
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a(n) = product(((-2)^(n-i+1)-1)/((-2)^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, -2], {n, 12, 20}] (* Vincenzo Librandi, Nov 06 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 12, -2) for n in xrange(12, 22)] # [From Zerinvary Lajos, May 28 2009]
(MAGMA) r:=12; q:=-2; [&*[(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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Diagonal k=12 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012
Sequence in context: A116461 A104699 A076575 * A260543 A145647 A251946
Adjacent sequences: A015420 A015421 A015422 * A015424 A015425 A015426
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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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