|
| |
|
|
A015277
|
|
Gaussian binomial coefficient [ n,3 ] for q=-9.
|
|
2
|
|
|
|
1, -656, 484210, -352504880, 257015284435, -187360965026144, 136586400868021924, -99571465386311288480, 72587599955185580267365, -52916360230556551635386480, 38576026619154398792076180886
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
3,2
|
|
|
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 = 3..200
Index entries for linear recurrences with constant coefficients, signature (-656,53874,478224,-531441).
|
|
|
FORMULA
|
G.f.: x^3/((1-x)*(1+9*x)*(1-81*x)*(1+729*x)). - Bruno Berselli, Oct 30 2012
a(n) = (-1+73*3^(4n-6)+(-1)^n*3^(2n-4)*(73-3^(4n-2)))/584000. - Bruno Berselli, Oct 30 2012
|
|
|
MATHEMATICA
|
Table[QBinomial[n, 3, -9], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *)
LinearRecurrence[{-656, 53874, 478224, -531441}, {1, -656, 484210, -352504880}, 20] (* Harvey P. Dale, Feb 10 2015 *)
|
|
|
PROG
|
(Sage) [gaussian_binomial(n, 3, -9) for n in xrange(3, 14)] # [From Zerinvary Lajos, May 27 2009]
|
|
|
CROSSREFS
|
Sequence in context: A252680 A233898 A088894 * A135418 A034818 A210091
Adjacent sequences: A015274 A015275 A015276 * A015278 A015279 A015280
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
Olivier Gérard
|
|
|
STATUS
|
approved
|
| |
|
|
