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A000487 Number of permutations of length n with exactly two valleys.
(Formerly M5022 N2165)
6
16, 272, 2880, 24576, 185856, 1304832, 8728576, 56520704, 357888000, 2230947840, 13754155008, 84134068224, 511780323328, 3100738912256, 18733264797696, 112949304754176, 680032201605120, 4090088616099840, 24582312700149760, 147669797096652800 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

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 = 5..200

C. J. Fewster, D. Siemssen, Enumerating Permutations by their Run Structure, arXiv preprint arXiv:1403.1723, 2014

R. G. Rieper and M. Zeleke, Valleyless Sequences

Index entries for linear recurrences with constant coefficients, signature (20,-160,656,-1456,1664,-768).

FORMULA

G.f.: 16x^5(1-3x)/((1-2x)^3*(1-4x)^2*(1-6x)). - Ralf Stephan, Sep 18 2003

a(n) = (6^n + (2 - 2n)4^n + (2n^2 - 4n - 1)2^n)/32. - Mitchell Harris, Apr 02 2004

MATHEMATICA

nn = 30; Drop[CoefficientList[Series[16 x^5 (1 - 3 x)/((1 - 2 x)^3*(1 - 4 x)^2*(1 - 6 x)), {x, 0, nn}], x], 5] (* T. D. Noe, Jun 20 2012 *)

CROSSREFS

Cf. A000431, A000517, A130651.

Column k=2 of A008303.

Sequence in context: A161595 A144660 A158574 * A249391 A197622 A002303

Adjacent sequences:  A000484 A000485 A000486 * A000488 A000489 A000490

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Ralf Stephan, Sep 18 2003

STATUS

approved

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Last modified August 17 15:18 EDT 2017. Contains 290635 sequences.