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A005283 Number of permutations of (1,...,n) having n-5 inversions (n>=5).

%I A005283 M3905 #29 Jun 29 2017 19:28:33
%S A005283 1,5,20,76,285,1068,4015,15159,57486,218895,836604,3208036,12337630,
%T A005283 47572239,183856635,712033264,2762629983,10736569602,41788665040,
%U A005283 162869776650,635562468075,2482933033659,9710010151831,38008957336974,148912655255315,583885852950802
%N A005283 Number of permutations of (1,...,n) having n-5 inversions (n>=5).
%C A005283 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
%D A005283 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 241.
%D A005283 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.14., p.356.
%D A005283 R. K. Guy, personal communication.
%D A005283 E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96.
%D A005283 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005283 G. C. Greubel, <a href="/A005283/b005283.txt">Table of n, a(n) for n = 5..1000</a>
%H A005283 R. K. Guy, <a href="/A000707/a000707_2.pdf">Letter to N. J. A. Sloane with attachment, Mar 1988</a>
%H A005283 B. H. Margolius, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/MARGOLIUS/inversions.html">Permutations with inversions</a>, J. Integ. Seqs. Vol. 4 (2001), #01.2.4.
%H A005283 R. H. Moritz and R. C. Williams, <a href="http://www.jstor.org/stable/2690326">A coin-tossing problem and some related combinatorics</a>, Math. Mag., 61 (1988), 24-29.
%F A005283 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
%e A005283 a(6)=5 because we have 213456, 132456, 124356, 123546, and 123465.
%p A005283 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
%t A005283 Table[SeriesCoefficient[Product[(1-x^j)/(1-x),{j,1,n}],{x,0,n-5}],{n,5,25}] (* _Vaclav Kotesovec_, Mar 16 2014 *)
%Y A005283 Cf. A008302, A000707, A001892, A001893, A001894, A005284, A005285, A048651.
%K A005283 nonn
%O A005283 5,2
%A A005283 _N. J. A. Sloane_
%E A005283 More terms, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), May 31 2001
%E A005283 Definition clarified by _Emeric Deutsch_, Aug 02 2014