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 A015359 Gaussian binomial coefficient [ n,8 ] for q=-4. 13
 1, 52429, 3665049245, 236497451900765, 15559876852907031645, 1018737244037427165087837, 66780267552779682073190144093, 4376244513647234644625387176712285, 286805936690898816904813999400193022045 (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 (52429,916249204,-3695444481856,-3798047410999296,972300137215819776,61999270288106192896,-1007426653738504290304,-3777907597814523756544,4722366482869645213696). FORMULA a(n) = Product_{i=1..8} ((-4)^(n-i+1)-1)/((-4)^i-1). - M. F. Hasler, Nov 03 2012 G.f.: -x^8 / ( (x-1)*(16384*x+1)*(4096*x-1)*(256*x-1)*(65536*x-1)*(64*x+1)*(4*x+1)*(16*x-1)*(1024*x+1) ). - R. J. Mathar, Sep 02 2016 MATHEMATICA Table[QBinomial[n, 8, -4], {n, 8, 20}] (* Vincenzo Librandi, Nov 02 2012 *) PROG (Sage) [gaussian_binomial(n, 8, -4) for n in range(8, 16)] # Zerinvary Lajos, May 25 2009 (Magma) r:=8; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012 (PARI) A015359(n, r=8, q=-4)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012 CROSSREFS Cf. A015356, A015357, A015360, A015361, A015363, A015364, A015365, A015367 A015368, A015369, A015370 (r=8, q=-2..-13). q=-4 integers/coefficients: A014985 (r=1), A015253 (r=2), A015271 (r=3), A015289 (r=4), A015308 (r=5), A015326 (r=6), A015341 (r=7), A015376 (r=9), A015390 (r=10), A015408 (r=11), A015425 (r=12). - M. F. Hasler, Nov 03 2012 Sequence in context: A346328 A345620 A346338 * A263123 A235237 A237138 Adjacent sequences: A015356 A015357 A015358 * A015360 A015361 A015362 KEYWORD nonn,easy AUTHOR Olivier Gérard STATUS approved

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Last modified May 30 04:46 EDT 2024. Contains 372958 sequences. (Running on oeis4.)