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Search: id:A001894
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| A001894 |
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Number of permutations by inversions.
(Formerly M3484 N1416)
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+0
3
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| 1, 4, 14, 49, 174, 628, 2298, 8504, 31758, 119483, 452284, 1720774, 6574987, 25214332, 96997223, 374153699, 1446677555, 5605337934, 21758936146, 84604366100, 329453055975, 1284626463105, 5015200610785, 19601107218591, 76685359017750, 300294650988857, 1176939165980809
(list; graph; listen)
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OFFSET
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4,2
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REFERENCES
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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.
R. K. Guy, personal communication.
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+3}/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-4), n=4..40);
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CROSSREFS
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Cf. A008302.
Sequence in context: A010904 A071737 A071741 this_sequence A079309 A026630 A034459
Adjacent sequences: A001891 A001892 A001893 this_sequence A001895 A001896 A001897
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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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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