OFFSET
7,1
REFERENCES
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 261.
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
T. D. Noe, Table of n, a(n) for n = 7..200
Désiré André, Mémoire sur les séquences des permutations circulaires, Bulletin de la S. M. F., tome 23 (1895), pp. 122-184.
C. J. Fewster, D. Siemssen, Enumerating Permutations by their Run Structure, arXiv preprint arXiv:1403.1723 [math.CO], 2014.
R. G. Rieper and M. Zeleke, Valleyless Sequences, arXiv:math/0005180 [math.CO], 2000.
Index entries for linear recurrences with constant coefficients, signature (40, -700, 7056, -45360, 194304, -561728, 1082624, -1332224, 946176, -294912).
FORMULA
G.f.: 16x^7(17-184x+636x^2-720x^3)/((1-2x)^4*(1-4x)^3*(1-6x)^2*(1-8x)). - Ralf Stephan, Sep 18 2003 [Proved by Désiré André, 1895, p.154, for circular permutations (see A008303). Peter Luschny, Aug 07 2019]
MATHEMATICA
nn = 20; Drop[CoefficientList[Series[16 x^7 (17 - 184 x + 636 x^2 - 720 x^3)/((1 - 2 x)^4*(1 - 4 x)^3*(1 - 6 x)^2*(1 - 8 x)), {x, 0, nn}], x], 7] (* T. D. Noe, Jun 20 2012 *)
LinearRecurrence[{40, -700, 7056, -45360, 194304, -561728, 1082624, -1332224, 946176, -294912}, {272, 7936, 137216, 1841152, 21253376, 222398464, 2174832640, 20261765120, 182172651520, 1594922762240}, 20] (* Jean-François Alcover, Feb 09 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Ralf Stephan, Sep 18 2003
STATUS
approved