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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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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.
Adjacent sequences: A001891 A001892 A001893 this_sequence A001895 A001896 A001897
Sequence in context: A010904 A071737 A071741 this_sequence A079309 A026630 A034459
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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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