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Search: id:A000707
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| A000707 |
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Number of permutations by inversions.
(Formerly M1646 N0644)
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+0
3
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| 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)
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OFFSET
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1,3
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REFERENCES
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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.
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LINKS
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B. H. Margolius, Permutations with inversions, J. Integ. Seqs. Vol. 4 (2001), #01.2.4.
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FORMULA
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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...
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CROSSREFS
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One of the diagonals of triangle in A008302.
Sequence in context: A049140 A092413 A047126 this_sequence A129777 A108600 A128729
Adjacent sequences: A000704 A000705 A000706 this_sequence A000708 A000709 A000710
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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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
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