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A000517 Number of permutations of length n with exactly three valleys.
(Formerly M5431 N2360)
9
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

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

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-Fran├žois 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

N. J. A. Sloane.

EXTENSIONS

More terms from Ralf Stephan, Sep 18 2003

STATUS

approved

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Last modified December 10 23:33 EST 2018. Contains 318049 sequences. (Running on oeis4.)