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A001251 Number of permutations of order n with the length of longest run equal 3.
(Formerly M2031 N0803)
12
0, 0, 2, 12, 70, 442, 3108, 24216, 208586, 1972904, 20373338, 228346522, 2763212980, 35926266244, 499676669254, 7405014187564, 116511984902094, 1940073930857802, 34087525861589564, 630296344519286304, 12235215845125112122, 248789737587365945992 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 262. (Terms for n>=13 are incorrect).

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

Max Alekseyev and Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 100 terms from Max Alekseyev)

Max A. Alekseyev, On the number of permutations with bounded runs length, arXiv preprint arXiv:1205.4581, 2012. - From N. J. A. Sloane, Oct 23 2012

FORMULA

a(n) ~ c * d^n * n!, where d = 0.924035857607536..., c = 1.25937125782834... . - Vaclav Kotesovec, Sep 06 2014

CROSSREFS

Cf. A001250, A001252, A001253, A010026, A211318.

Sequence in context: A116398 A001542 A059229 * A143357 A012426 A012421

Adjacent sequences:  A001248 A001249 A001250 * A001252 A001253 A001254

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Corrected and extended by Max Alekseyev at suggestion of Sean A. Irvine, May 04 2012

STATUS

approved

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Last modified October 24 06:43 EDT 2017. Contains 293836 sequences.