A015393 Gaussian binomial coefficient [ n,10 ] for q=-7.

1, 247165843, 71272779562356450, 20074270583791406305395150, 5672847283550509352791825564114953, 1602343611088456383646516751967506297398179, 452626257785468649545785666454333613632908777305800

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

Vincenzo Librandi, Table of n, a(n) for n = 10..130

Formula

a(n) = Product_{i=1..10} ((-7)^(n-i+1)-1)/((-7)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 10, -7], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Sage) [gaussian_binomial(n, 10, -7) for n in range(10, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-7; [&*[(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, A015390, A015391, A015392, A015394, A015397, A015398, A015399, A015401, A015402. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A033626 A234377 A210020 * A262989 A119859 A119860

Adjacent sequences: A015390 A015391 A015392 * A015394 A015395 A015396

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved