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 A186762 Number of permutations of {1,2,...,n} having no increasing odd cycles. 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)
 1, 0, 1, 1, 9, 33, 235, 1517, 12593, 111465, 1122819, 12313409, 147949593, 1922353925, 26918452691, 403744456541, 6460109224801, 109820584161393, 1976779056442179, 37558742545087481, 751175283283221129, 15774677696321630525, 347042934659313999539, 7981987292809647817237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(n) = A186761(n,0). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..450 FORMULA E.g.f.: g(z) = exp(-sinh z)/(1-z). a(n) ~ exp(-sinh(1)) * n! = 0.308756853522... * n!. - Vaclav Kotesovec, Mar 16 2014 EXAMPLE a(3)=1 because we have (132). a(4)=9 because we have (12)(34), (13)(24), (14)(23), and the six cyclic permutations of {1,2,3,4}. MAPLE g := exp(-sinh(z))/(1-z): gser := series(g, z = 0, 27): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 23); # second Maple program: a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)* ((j-1)!-irem(j, 2))*binomial(n-1, j-1), j=1..n)) end: seq(a(n), n=0..23); # Alois P. Heinz, May 04 2023 MATHEMATICA CoefficientList[Series[E^(-Sinh[x])/(1-x), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Mar 16 2014 *) CROSSREFS Cf. A186761, A186763, A186764, A186765, A186766, A186769. Sequence in context: A146445 A046997 A013488 * A343843 A063423 A183939 Adjacent sequences: A186759 A186760 A186761 * A186763 A186764 A186765 KEYWORD nonn AUTHOR Emeric Deutsch, Feb 27 2011 STATUS approved

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Last modified September 30 21:59 EDT 2023. Contains 365812 sequences. (Running on oeis4.)