A015397 Gaussian binomial coefficient [ n,10 ] for q=-9.

1, 3138105961, 11078672649879436966, 38576026619154398792076180886, 134526791875519431052113309866825757301, 469057975890128020293538941741406421614821552253, 1635507110993502253670495254060345828123783573932476807608

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..110

Formula

a(n) = Product_{i=1..10} ((-9)^(n-i+1)-1)/((-9)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 10, -9], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Sage) [gaussian_binomial(n, 10, -9) for n in range(10, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-9; [&*[(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, A015393, A015394, A015398, A015399, A015401, A015402. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A203886 A257914 A257893 * A291600 A092380 A096566

Adjacent sequences: A015394 A015395 A015396 * A015398 A015399 A015400

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved