The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000517 Number of permutations of length n with exactly three valleys. (Formerly M5431 N2360) 7
 272, 7936, 137216, 1841152, 21253376, 222398464, 2174832640, 20261765120, 182172651520, 1594922762240, 13684856848384, 115620218667008, 965271355195392, 7984436548730880, 65569731961159680, 535438370914959360, 4353038473793372160, 35266789418949672960 (list; graph; refs; listen; history; text; internal format)
 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. 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 Cf. A000431, A000487. Column k=3 of A008303. Sequence in context: A316930 A317701 A141546 * A250341 A168372 A023907 Adjacent sequences:  A000514 A000515 A000516 * A000518 A000519 A000520 KEYWORD nonn AUTHOR EXTENSIONS More terms from Ralf Stephan, Sep 18 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 18 10:54 EDT 2021. Contains 345098 sequences. (Running on oeis4.)