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 A001894 Number of permutations of {1,...,n} having n-4 inversions (n>=4). (Formerly M3484 N1416) 6
 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; refs; listen; history; text; internal format)
 OFFSET 4,2 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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). 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 = 4..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. E. Netto, Lehrbuch der Combinatorik, Chapter 4, annotated scanned copy of pages 92-99 only. FORMULA a(n) = 2^(2*n-5)/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(5)=4  because we have 21345, 13245, 12435, and 12354. MAPLE 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); # Barbara Haas Margolius, May 31 2001 MATHEMATICA Table[SeriesCoefficient[Product[(1-x^j)/(1-x), {j, 1, n}], {x, 0, n-4}], {n, 4, 25}] (* Vaclav Kotesovec, Mar 16 2014 *) CROSSREFS Cf. A008302, A048651. Sequence in context: A211305 A316974 A278026 * A215493 A079309 A026630 Adjacent sequences:  A001891 A001892 A001893 * A001895 A001896 A001897 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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Last modified October 15 21:17 EDT 2019. Contains 328038 sequences. (Running on oeis4.)