A015368 Gaussian binomial coefficient [ n,8 ] for q=-11.

1, 196495641, 42471590605551405, 9097327679593690752247605, 1950226184559914695131839252162415, 418045706884240723248900544124967821025015, 89611860518118688087749643530422009144522097477435

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

Vincenzo Librandi, Table of n, a(n) for n = 8..100

Formula

a(n) = Product_{i=1..8} ((-11)^(n-i+1)-1)/((-11)^i-1). - M. F. Hasler, Nov 03 2012

Mathematica

Table[QBinomial[n, 8, -11], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)

Prog

(Sage) [gaussian_binomial(n, 8, -11) for n in range(8, 14)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=-11; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012
(PARI) A015368(n, r=8, q=-11)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

Crossrefs

Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015369, A015370. - M. F. Hasler, Nov 03 2012

Sequence in context: A209597 A251514 A268844 * A317287 A132205 A358019

Adjacent sequences: A015365 A015366 A015367 * A015369 A015370 A015371

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved