OFFSET
0,5
COMMENTS
a(n) = A186363(n,0).
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..198
Emeric Deutsch and Sergi Elizalde, Cycle up-down permutations, arXiv:0909.5199 [math.CO], 2009; and also, Australas. J. Combin. 50 (2011), 187-199.
FORMULA
E.g.f.: exp(-z)/(1-sin(z)).
G.f.: 1/(1-x^2/(1-x-3*x^2/(1-2*x-6*x^2/(1-3*x-10*x^2/(1-.../(1-n*x-((n+1)*(n+2)/2)*x^2/(1-... (continued fraction). - Paul Barry, Apr 11 2011
a(n) ~ n! * n * exp(-Pi/2) * 2^(n+3) / Pi^(n+2). - Vaclav Kotesovec, Oct 08 2013
G.f.: conjecture: T(0), where T(k) = 1 - x^2*(k+1)*(k+2)/(x^2*(k+1)*(k+2) - 2*(1-x*k)*(1-x*(k+1))/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 21 2013
EXAMPLE
a(4) = 5 because we have (12)(34),(13)(24),(1324),(1423), and (14)(23).
MAPLE
g := exp(-z)/(1-sin(z)): gser := series(g, z = 0, 28): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 24);
MATHEMATICA
CoefficientList[Series[E^(-x)/(1-Sin[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 08 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 28 2011
STATUS
approved