|
| |
|
|
A006102
|
|
Gaussian binomial coefficient [ n,4 ] for q=3.
(Formerly M5384)
|
|
1
| |
|
|
1, 121, 11011, 925771, 75913222, 6174066262, 500777836042, 40581331447162, 3287582741506063, 266307564861468823, 21571273555248777493, 1747282899667791058573, 141530177899268957392924, 11463951511551877750726204, 928580264181940191843785764, 75215006575885931519565302404
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 4,2
|
|
|
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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=4..100
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
|
|
|
MAPLE
| A006102:=-1/((z-1)*(81*z-1)*(3*z-1)*(9*z-1)*(27*z-1)); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
|
|
|
PROG
| (Other) sage: [gaussian_binomial(n, 4, 3) for n in xrange(4, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2009]
|
|
|
CROSSREFS
| Sequence in context: A144766 A176923 A058412 * A036508 A054319 A006061
Adjacent sequences: A006099 A006100 A006101 * A006103 A006104 A006105
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
