|
Search: id:A000707
|
|
|
| A000707 |
|
Number of permutations by inversions.
(Formerly M1646 N0644)
|
|
+0
3
|
|
| 1, 1, 2, 6, 20, 71, 259, 961, 3606, 13640, 51909, 198497, 762007, 2934764, 11333950, 43874857, 170193528, 661386105, 2574320659, 10034398370, 39163212165, 153027659730, 598577118991, 2343628878849, 9184197395425, 36020235035016
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 241.
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, p. 15.
R. H. Moritz and R. C. Williams, A coin-tossing problem and some related combinatorics, Math. Mag., 61 (1988), 24-29.
E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96.
|
|
LINKS
|
B. H. Margolius, Permutations with inversions, J. Integ. Seqs. Vol. 4 (2001), #01.2.4.
|
|
FORMULA
|
See A008302 for G.f.
a(n)=2^{2n}/sqrt{pi n}Q(1+O(n^{-1})) where Q is a digital search tree constant, Q = 0.2887880951...
|
|
CROSSREFS
|
One of the diagonals of triangle in A008302.
Sequence in context: A151286 A047126 A145138 this_sequence A129777 A108600 A128729
Adjacent sequences: A000704 A000705 A000706 this_sequence A000708 A000709 A000710
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 16 1999
Asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 5/31/01
|
|
|
Search completed in 0.002 seconds
|
