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Search: id:A001893
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| A001893 |
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Number of permutations by inversions.
(Formerly M2810 N1132)
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+0
3
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| 1, 3, 9, 29, 98, 343, 1230, 4489, 16599, 61997, 233389, 884170, 3366951, 12876702, 49424984, 190297064, 734644291, 2842707951, 11022366544, 42815701060, 166583279325, 649063995030, 2532267577126, 9891097066760, 38676401680776, 151381995733542, 593053313030007
(list; graph; listen)
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OFFSET
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3,2
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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.
R. K. Guy, personal communication.
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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a(n)=2^{2n+2}/sqrt{pi n}Q(1+O(n^{-1})) where Q is a digital search tree constant, Q = 0.2887880951...
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MAPLE
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f := (x, n)->product((1-x^j)/(1-x), j=1..n); seq(coeff(series(f(x, n), x, n+2), x, n-3), n=3..40);
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CROSSREFS
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Cf. A008302.
Adjacent sequences: A001890 A001891 A001892 this_sequence A001894 A001895 A001896
Sequence in context: A081696 A148939 A077587 this_sequence A151030 A066331 A099780
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms, Maple code, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 5/31/01
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