OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
E. Deutsch and S. Elizalde, Cycle up-down permutations, arXiv:0909.5199 [math.CO], 2009.
FORMULA
E.g.f.: -log(1-sin(z)) / (1-sin(z)).
a(n) = Sum_{k=1..n} k*A186366(n,k).
a(n) ~ n!*n*2^(n+3)/Pi^(n+2)*(2*log(n/Pi) + 2*gamma + 3*log(2) - 2), where gamma is the Euler-Mascheroni constant (A001620). - Vaclav Kotesovec, Oct 02 2013
EXAMPLE
a(3) = 10 because the cycle-up-down permutations (1)(2)(3), (12)(3), (13)(2), (1)(23), and (132), have a total of 3+2+2+2+1=10 cycles.
MAPLE
g := -ln(1-sin(z))/(1-sin(z)): gser := series(g, z = 0, 25): seq(factorial(n)*coeff(gser, z, n), n = 1 .. 22);
MATHEMATICA
Rest[CoefficientList[Series[-Log[1-Sin[x]]/(1-Sin[x]), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 02 2013 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(-log(1-sin(x))/(1-sin(x)))) \\ G. C. Greubel, Aug 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 28 2011
STATUS
approved