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A015390 Gaussian binomial coefficient [ n,10 ] for q=-4. 14
1, 838861, 938250090141, 968690748238618461, 1019729183363623510391901, 1068220365220113899181567068253, 1120383768613759382944995805859747933, 1174735830441360695151745376566623493806173, 1231818594183047090443637654682442929123639613533 (list; graph; refs; listen; history; text; internal format)
OFFSET
10,2
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
FORMULA
a(n) = Product_{i=1..10} ((-4)^(n-i+1)-1)/((-4)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012
G.f.: x^10 / ((x-1) * (4*x+1) * (16*x-1) * (64*x+1) * (256*x-1) * (1024*x+1) * (4096*x-1) * (16384*x+1) * (65536*x-1) * (262144*x+1) * (1048576*x-1)). - Colin Barker, Jan 13 2014
MATHEMATICA
Table[QBinomial[n, 10, -4], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)
PROG
(Sage) [gaussian_binomial(n, 10, -4) for n in range(10, 17)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 04 2012
CROSSREFS
Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015391, A015392, A015393, A015394, A015397, A015398, A015399, A015401, A015402. - Vincenzo Librandi, Nov 04 2012
Sequence in context: A254817 A305827 A113150 * A263038 A043623 A185520
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)