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A015370
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Gaussian binomial coefficient [ n,8 ] for q=-13.
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23
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1, 757464241, 621564749363392901, 506798783502833908602716981, 413425812255544017749839936272484623, 337243227617163445881817693983677965955870943, 275099718210633054941121644140453635236773122223471523
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OFFSET
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8,2
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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 = 8..100
Index entries related to Gaussian binomial coefficients.
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FORMULA
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a(n)=product_{i=1..8} ((-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, 8, -13], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 8, -13) for n in xrange(8, 14)] # [From Zerinvary Lajos, May 25 2009]
(MAGMA) r:=8; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
(PARI) A015370(n, r=8, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ - M. F. Hasler, Nov 03 2012
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CROSSREFS
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Cf. Gaussian binomial coefficients [n,8] for q=-2,...,-12: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015369. - M. F. Hasler, Nov 03 2012
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), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012
Sequence in context: A244186 A035518 A104952 * A068725 A104932 A118876
Adjacent sequences: A015367 A015368 A015369 * A015371 A015372 A015373
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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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