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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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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