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 A202013 The number of functions f:{1,2,...,n}->{1,2,...,n} that have an odd number of odd length cycles and no even length cycles. 1
 0, 1, 2, 12, 100, 1120, 15606, 260344, 5056136, 112026240, 2788230250, 77009739136, 2337124786668, 77302709780608, 2767629599791070, 106631592312384000, 4398877912885363216, 193450993635808976896, 9034380526387410161874, 446519425974262943518720, 23284829853408862172112500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The number of endofunctions with an odd number of recurrent elements. It appears that almost all endofunctions have an even number of recurrent elements. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..386 FORMULA E.g.f.: sinh(log(((1-LambertW(-x))/(1+LambertW(-x)))^(1/2))). - corrected by Vaclav Kotesovec, Sep 24 2013 a(n) ~ n! * 2^(3/4)*Gamma(3/4)*exp(n)/(4*Pi*n^(3/4)) * (1+7*Pi/(24*Gamma(3/4)^2*sqrt(n))). - Vaclav Kotesovec, Sep 24 2013 MAPLE b:= proc(n, t) option remember; `if`(n=0, t, add( `if`(j::odd, (j-1)!*b(n-j, 1-t)* binomial(n-1, j-1), 0), j=1..n)) end: a:= n-> add(b(j, 0)*n^(n-j)*binomial(n-1, j-1), j=0..n): seq(a(n), n=0..20); # Alois P. Heinz, May 20 2016 MATHEMATICA t = Sum[n^(n - 1) x^n/n!, {n, 1, 20}]; Range[0, 20]! CoefficientList[Series[Sinh[Log[((1 + t)/(1 - t))^(1/2)]], {x, 0, 20}], x] CoefficientList[Series[(((1-LambertW[-x])/(1+LambertW[-x]))^(1/2))/2 - 1/(2*((1-LambertW[-x])/(1+LambertW[-x]))^(1/2)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 24 2013 *) CROSSREFS Cf. A060435, A116956. Sequence in context: A168365 A055865 A085389 * A151505 A096347 A137483 Adjacent sequences: A202010 A202011 A202012 * A202014 A202015 A202016 KEYWORD nonn AUTHOR Geoffrey Critzer, Dec 08 2011 STATUS approved

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Last modified April 12 16:45 EDT 2024. Contains 371635 sequences. (Running on oeis4.)