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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)
 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.)