cp's OEIS Frontend

A001893 Number of permutations of (1,...,n) having n-3 inversions (n>=3).

%I A001893 M2810 N1132 #36 Jun 29 2017 19:23:24
%S A001893 1,3,9,29,98,343,1230,4489,16599,61997,233389,884170,3366951,12876702,
%T A001893 49424984,190297064,734644291,2842707951,11022366544,42815701060,
%U A001893 166583279325,649063995030,2532267577126,9891097066760,38676401680776,151381995733542,593053313030007
%N A001893 Number of permutations of (1,...,n) having n-3 inversions (n>=3).
%C A001893 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 A001893 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 241.
%D A001893 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.14., p.356.
%D A001893 R. K. Guy, personal communication.
%D A001893 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, p. 15.
%D A001893 E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96.
%D A001893 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001893 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001893 G. C. Greubel, <a href="/A001893/b001893.txt">Table of n, a(n) for n = 3..1000</a>
%H A001893 R. K. Guy, <a href="/A000707/a000707_2.pdf">Letter to N. J. A. Sloane with attachment, Mar 1988</a>
%H A001893 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 A001893 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.
%H A001893 E. Netto, <a href="/A000707/a000707_1.pdf">Lehrbuch der Combinatorik</a>, Chapter 4, annotated scanned copy of pages 92-99 only.
%F A001893 a(n) = 2^(2*n-4)/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 A001893 a(4)=3  because we have 1243, 1324, and 2134.
%p A001893 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); # Barbara Haas Margolius, May 31 2001
%t A001893 Table[SeriesCoefficient[Product[(1-x^j)/(1-x),{j,1,n}],{x,0,n-3}],{n,3,25}] (* _Vaclav Kotesovec_, Mar 16 2014 *)
%Y A001893 Cf. A008302, A048651.
%K A001893 nonn
%O A001893 3,2
%A A001893 _N. J. A. Sloane_
%E A001893 More terms, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), May 31 2001
%E A001893 Definition clarified by _Emeric Deutsch_, Aug 02 2014