OFFSET
2,2
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.
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 = 2..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-3)/sqrt(Pi*n)*Q*(1+O(n^{-1})), where Q is a digital search tree constant, Q = 0.288788095... (see A048651). - corrected by Vaclav Kotesovec, Mar 16 2014
EXAMPLE
a(4)=5 because we have 1342, 1423, 2143, 2314, and 3124.
MAPLE
f := (x, n)->product((1-x^j)/(1-x), j=1..n); seq(coeff(series(f(x, n), x, n+2), x, n-2), n=2..40);
MATHEMATICA
Table[SeriesCoefficient[Product[(1-x^j)/(1-x), {j, 1, n}], {x, 0, n-2}], {n, 2, 25}] (* Vaclav Kotesovec, Mar 16 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms, Maple code, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), May 31 2001
Definition clarified by Emeric Deutsch, Aug 02 2014
STATUS
approved