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A015422
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Gaussian binomial coefficient [ n,11 ] for q=-13.
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12
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1, -1664148937320, 3000174326048697741925710, -5374347381421937558314402513609688760, 9632029764916740618771445568833182996026908640493, -17262095767026556801586191040816999767731925288888540910160480
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OFFSET
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11,2
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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 = 11..90
Index entries related to Gaussian binomial coefficients.
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FORMULA
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a(n) = product_{i=1..11} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012
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MATHEMATICA
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Table[QBinomial[n, 11, -13], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 11, -13) for n in xrange(11, 16)] # - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009
(PARI) A015422(n, r=11, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ - M. F. Hasler, Nov 03 2012
(MAGMA) r:=11; q:=-13; [&*[(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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Cf. Gaussian binomial coefficients [n,r] for q=-13: A015265 (r=2), A015286 (r=3), A015303 (r=4), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015438 (r=12). - M. F. Hasler, Nov 03 2012
Sequence in context: A213601 A213646 A172799 * A017543 A032756 A026081
Adjacent sequences: A015419 A015420 A015421 * A015423 A015424 A015425
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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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