A122647 Number of permutations of length 2*n-1 with no local maxima or minima in even positions.

1, 2, 14, 204, 5104, 195040, 10570416, 771171296, 72871890176, 8658173200896, 1263326817241600, 222078432102900736, 46291130226003357696, 11289508838355990634496, 3184719803676823556888576, 1028950134725811309304442880, 377483869192551997938994315264, 156057810922284533544621710639104

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..246

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

CF. A113583, A261683.

Sequence in context: A279452 A262008 A054652 * A158097 A262003 A271847

Adjacent sequences: A122644 A122645 A122646 * A122648 A122649 A122650

Keyword

nonn

Author

N. J. A. Sloane, Sep 21 2006

Status

approved