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A186359
Number of permutations of {1,2,...,n} having no up-down cycles. A cycle (b(1), b(2), ...) is said to be up-down if, when written with its smallest element in the first position, it satisfies b(1)<b(2)>b(3)<... .
2
1, 0, 0, 1, 4, 19, 114, 799, 6392, 57527, 575270, 6327971, 75935652, 987163475, 13820288650, 207304329751, 3316869276016, 56386777692271, 1014961998460878, 19284277970756683, 385685559415133660, 8099396747717806859, 178186728449791750898
OFFSET
0,5
COMMENTS
a(n)=A186358(n,0).
LINKS
E. Deutsch and S. Elizalde, Cycle up-down permutations, arXiv:0909.5199v1 [math.CO].
FORMULA
E.g.f.=(1-sin z)/(1-z).
a(2m-1)=(2m-1)!*Sum((-1)^j/(2j-1)!, j=2..m).
a(2m)=(2m)!*Sum((-1)^j/(2j-1)!, j=2..m).
a(n) ~ n! * (1-sin(1)). - Vaclav Kotesovec, Oct 02 2013
EXAMPLE
a(4)=4 because we have (1432), (1342), (1243), and (1234).
MAPLE
g := (1-sin(z))/(1-z): gser := series(g, z = 0, 25): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 22);
MATHEMATICA
CoefficientList[Series[(1-Sin[x])/(1-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 02 2013 *)
CROSSREFS
Sequence in context: A122835 A013185 A353607 * A203268 A209673 A261497
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 28 2011
STATUS
approved