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 A015356 Gaussian binomial coefficient [ n,8 ] for q=-2. 14
 1, 171, 58311, 13275471, 3624203583, 899790907743, 233988483199263, 59438516325245343, 15275698695588053151, 3902985682508407194271, 1000137219716325891620511, 255910660218571393553843871 (list; graph; refs; listen; history; text; internal format)
 OFFSET 8,2 REFERENCES 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. LINKS Vincenzo Librandi, Table of n, a(n) for n = 8..200 Index entries for linear recurrences with constant coefficients, signature (171,29070,-1666680,-56000448,896007168,6826721280,-30482104320,-45902462976,68719476736). FORMULA a(n) = Product_{i=1..8} ((-2)^(n-i+1)-1)/((-2)^i-1). - M. F. Hasler, Nov 03 2012 G.f.: -x^8 / ( (x-1)*(64*x-1)*(128*x+1)*(2*x+1)*(8*x+1)*(32*x+1)*(16*x-1)*(4*x-1)*(256*x-1) ). - R. J. Mathar, Sep 02 2016 MATHEMATICA Table[QBinomial[n, 8, -2], {n, 8, 20}] (* Vincenzo Librandi, Nov 02 2012 *) PROG (Sage) [gaussian_binomial(n, 8, -2) for n in range(8, 20)] # Zerinvary Lajos, May 25 2009 (MAGMA) r:=8; q:=-2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 02 2012 (PARI) A015356(n, r=8, q=-2)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012 CROSSREFS Cf. Gaussian binomial coefficients [n,8] for q=-3..-13: A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015369, A015370. - M. F. Hasler, Nov 03 2012 Diagonal k=8 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012 Sequence in context: A145625 A097844 A076573 * A259158 A252139 A252132 Adjacent sequences:  A015353 A015354 A015355 * A015357 A015358 A015359 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified August 9 11:08 EDT 2020. Contains 336323 sequences. (Running on oeis4.)