A015391 Gaussian binomial coefficient [ n,10 ] for q=-5.

1, 8138021, 82784230211046, 802023560334345174046, 7844813030956382105126218421, 76584995059524711257676812461230921, 747948211058777330441088769852487456090296, 7304088256300765454892487244083619479306573590296, 71329169480592334495874625222480141259420027767138434046

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..150

Formula

a(n) = Product_{i=1..10} ((-5)^(n-i+1)-1)/((-5)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 10, -5], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(SageMath) [gaussian_binomial(n, 10, -5) for n in range(10, 17)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-5; [&*[(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, A015392, A015393, A015394, A015397, A015398, A015399, A015401, A015402.

Sequence in context: A263072 A353540 A183020 * A277580 A059693 A083629

Adjacent sequences: A015388 A015389 A015390 * A015392 A015393 A015394

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved