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A186760 Number of cycles that are either nonincreasing or of length 1 in all permutations of {1,2,...,n}. A cycle (b(1), b(2), ...) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<... . 7
0, 1, 2, 7, 33, 188, 1247, 9448, 80623, 765926, 8022139, 91872328, 1142384735, 15330003154, 220847064955, 3399884265524, 55705822616383, 967921774366510, 17778279366693179, 344189681672898400, 7005438733866799999, 149547115419379439978, 3341127481398057119515 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = Sum(A186759(n,k), k=0..n).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

E.g.f.: (1+z-exp(z)-log(1-z))/(1-z).

a(n) ~ n! * (log(n) + gamma + 2 - exp(1)), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Oct 08 2013

EXAMPLE

a(3) = 7 because in (1)(2)(3), (1)(23), (12)(3), (13)(2), (123), and (132) we have a total of 3 + 1 + 1 + 1 + 0 + 1 = 7 cycles that are either of length 1 or nonincreasing.

MAPLE

g := (1+z-exp(z)-ln(1-z))/(1-z): gser := series(g, z = 0, 25): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 22);

MATHEMATICA

CoefficientList[Series[(1+x-E^x-Log[1-x])/(1-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 08 2013 *)

CROSSREFS

Cf. A186754, A186755, A186756, A186757, A186758, A186759.

Sequence in context: A302285 A249636 A172387 * A162661 A299043 A104981

Adjacent sequences:  A186757 A186758 A186759 * A186761 A186762 A186763

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 26 2011

STATUS

approved

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Last modified April 12 11:25 EDT 2021. Contains 342920 sequences. (Running on oeis4.)