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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; text; 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
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
MAPLE
A006102:=-1/((z-1)*(81*z-1)*(3*z-1)*(9*z-1)*(27*z-1)); # conjectured (correctly) by Simon Plouffe in his 1992 dissertation
MATHEMATICA
Table[QBinomial[n, 4, 3], {n, 4, 24}] (* Vincenzo Librandi, Aug 02 2016 *)
PROG
(Sage) [gaussian_binomial(n, 4, 3) for n in range(4, 20)] # Zerinvary Lajos, May 25 2009
(Magma) r:=4; q:=3; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016
CROSSREFS
Partial sums of A226804. - Christian Krause, Dec 26 2022
Sequence in context: A176923 A058412 A231661 * A263819 A036508 A054319
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 20 12:14 EDT 2024. Contains 371838 sequences. (Running on oeis4.)