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A001267 One-half the number of permutations of length n with exactly 3 rising or falling successions.
(Formerly M4550 N1934)
7
0, 0, 0, 0, 1, 8, 60, 444, 3599, 32484, 325322, 3582600, 43029621, 559774736, 7841128936, 117668021988, 1883347579515, 32026067455084, 576605574327174, 10957672400252944, 219190037987444577, 4603645435776504120, 101292568208941883236, 2329975164242735146316 (list; graph; refs; listen; history; internal format)
OFFSET

0,6

COMMENTS

(1/2) times number of permutations of 12...n such that exactly 3 of the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263.

J. Riordan, A recurrence for permutations without rising or falling successions. Ann. Math. Statist. 36 (1965), 708-710.

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).

FORMULA

Coefficient of t^3 in S[n](t) defined in A002464, divided by 2.

CROSSREFS

Cf. A002464, A000130, A086852. Equals A086854/2. A diagonal of A010028.

Sequence in context: A093132 A094169 A129325 * A099156 A199526 A129331

Adjacent sequences:  A001264 A001265 A001266 * A001268 A001269 A001270

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 16 23:45 EST 2012. Contains 205978 sequences.