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 A005285 Number of permutations of (1,...,n) having n-7 inversions (n>=7). (Formerly M4414) 5
 1, 7, 35, 155, 649, 2640, 10569, 41926, 165425, 650658, 2554607, 10020277, 39287173, 154022930, 603919164, 2368601685, 9293159292, 36476745510, 143239635450, 562744102479, 2211876507387, 8697839966552, 34218338900591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 7,2 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 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 = 7..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-8)/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(8)=7 because we have 21345678, 13245678, 12435678, 12354678, 12346578, 12345768, and 12345687. MAPLE g := proc(n, k) option remember; if k=0 then return(1) else if (n=1 and k=1) then return(0) else if (k<0 or k>binomial(n, 2)) then return(0) else g(n-1, k)+g(n, k-1)-g(n-1, k-n) end if end if end if end proc; seq(g(j+7, j), j=0..30); # Barbara Haas Margolius, May 31 2001 MATHEMATICA Table[SeriesCoefficient[Product[(1-x^j)/(1-x), {j, 1, n}], {x, 0, n-7}], {n, 7, 25}] (* Vaclav Kotesovec, Mar 16 2014 *) CROSSREFS Cf. A008302, A000707, A001892, A001893, A001894, A005283, A005284, A048651. Sequence in context: A022635 A217274 A000588 * A006095 A171477 A265612 Adjacent sequences:  A005282 A005283 A005284 * A005286 A005287 A005288 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 January 21 15:59 EST 2019. Contains 319350 sequences. (Running on oeis4.)