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 A005283 Number of permutations of (1,...,n) having n-5 inversions (n>=5). (Formerly M3905) 5
 1, 5, 20, 76, 285, 1068, 4015, 15159, 57486, 218895, 836604, 3208036, 12337630, 47572239, 183856635, 712033264, 2762629983, 10736569602, 41788665040, 162869776650, 635562468075, 2482933033659, 9710010151831, 38008957336974, 148912655255315, 583885852950802 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 COMMENTS Sequence is a diagonal of the triangle A008302 (number of permutations of (1,...,n) with k inversions; see Table 1 of the Margolius reference). - Emeric Deutsch, Aug 02 2014 REFERENCES F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 241. S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.14., p.356. R. K. Guy, personal communication. E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 5..1000 B. H. Margolius, Permutations with inversions, J. Integ. Seqs. Vol. 4 (2001), #01.2.4. R. H. Moritz and R. C. Williams, A coin-tossing problem and some related combinatorics, Math. Mag., 61 (1988), 24-29. FORMULA a(n) = 2^(2*n-6)/sqrt(Pi*n)*Q*(1+O(n^{-1})), where Q is a digital search tree constant, Q = 0.2887880951... (see A048651). - corrected by Vaclav Kotesovec, Mar 16 2014 EXAMPLE a(6)=5 because we have 213456, 132456, 124356, 123546, and 123465. MAPLE f := (x, n)->product((1-x^j)/(1-x), j=1..n); seq(coeff(series(f(x, n), x, n+2), x, n-5), n=5..40); # Barbara Haas Margolius, May 31 2001 MATHEMATICA Table[SeriesCoefficient[Product[(1-x^j)/(1-x), {j, 1, n}], {x, 0, n-5}], {n, 5, 25}] (* Vaclav Kotesovec, Mar 16 2014 *) CROSSREFS Cf. A008302, A000707, A001892, A001893, A001894, A005284, A005285, A048651. Sequence in context: A270023 A061278 A000758 * A057552 A300918 A269708 Adjacent sequences:  A005280 A005281 A005282 * A005284 A005285 A005286 KEYWORD nonn AUTHOR EXTENSIONS More terms, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), May 31 2001 Definition clarified by Emeric Deutsch, Aug 02 2014 STATUS approved

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