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A001893 Number of permutations by inversions.
(Formerly M2810 N1132)
+0
3
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)
OFFSET

3,2

REFERENCES

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.

LINKS

B. H. Margolius, Permutations with inversions, J. Integ. Seqs. Vol. 4 (2001), #01.2.4.

FORMULA

a(n)=2^{2n+2}/sqrt{pi n}Q(1+O(n^{-1})) where Q is a digital search tree constant, Q = 0.2887880951...

MAPLE

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);

CROSSREFS

Cf. A008302.

Adjacent sequences: A001890 A001891 A001892 this_sequence A001894 A001895 A001896

Sequence in context: A081696 A148939 A077587 this_sequence A151030 A066331 A099780

KEYWORD

nonn

AUTHOR

njas

EXTENSIONS

More terms, Maple code, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 5/31/01

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Last modified January 7 11:41 EST 2009. Contains 152824 sequences.


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