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A122647 Number of permutations of length 2*n-1 with no local maxima or minima in even positions. 3
1, 2, 14, 204, 5104, 195040, 10570416, 771171296, 72871890176, 8658173200896, 1263326817241600, 222078432102900736, 46291130226003357696, 11289508838355990634496, 3184719803676823556888576, 1028950134725811309304442880, 377483869192551997938994315264, 156057810922284533544621710639104 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
D. E. Knuth, Whirlpool Permutations, May 05 2020
M. La Croix, A combinatorial proof of a result of Gessel and Greene, Discr. Math., 306 (2006), 2251-2256.
Jiaxi Lu and Yuanzhe Ding, A skeleton model to enumerate standard puzzle sequences, arXiv:2106.09471 [math.CO], 2021.
FORMULA
a(n) = A113583(n)/2^(n-1).
MAPLE
egf:= (x->1/(1-x*tanh(x))-1)(z/sqrt(2)):
a:= n-> (2*n)!/n*coeff(series(egf, z, 2*n+1), z, 2*n):
seq(a(n), n=1..18); # Alois P. Heinz, Oct 05 2021
CROSSREFS
Sequence in context: A279452 A262008 A054652 * A158097 A262003 A271847
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 21 2006
STATUS
approved

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Last modified February 28 17:13 EST 2024. Contains 370400 sequences. (Running on oeis4.)