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A015361
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Gaussian binomial coefficient [ n,8 ] for q=-6.
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13
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1, 1439671, 2487182817955, 4158260859792814555, 6989674736616919292088715, 11738459947705882553575280369515, 19716527736890127515275338116221320235, 33116077152651051199781730118147946460139435, 55622326158904300663023790195853299389540017396395
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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..170
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FORMULA
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a(n) = Product_{i=1..8} ((-6)^(n-i+1)-1)/((-6)^i-1). - M. F. Hasler, Nov 03 2012
G.f.: -x^8 / ( (x-1)*(279936*x+1)*(216*x+1)*(36*x-1)*(7776*x+1)*(1296*x-1)*(6*x+1)*(46656*x-1)*(1679616*x-1) ). - R. J. Mathar, Sep 02 2016
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MATHEMATICA
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Table[QBinomial[n, 8, -6], {n, 8, 19}] (* Vincenzo Librandi, Nov 03 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 8, -6) for n in range(8, 15)] # Zerinvary Lajos, May 25 2009
(MAGMA) r:=8; q:=-6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
(PARI) A015361(n, r=8, q=-6)=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..-13: A015356, A015357, A015359, A015360, A015363, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012
Sequence in context: A346355 A339477 A234657 * A259306 A210629 A156621
Adjacent sequences: A015358 A015359 A015360 * A015362 A015363 A015364
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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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