OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
R. P. Stanley, Permutations, Joint Mathematics Meeting, 2009.
R. P. Stanley, Alternating permutations and symmetric functions, J. Comb. Theory A 114 (3) (2007) 436-460
FORMULA
G.f.: (1-x^2)^{-1/4} (1+x)^{-1/2} Sum_{k>=0} E_{2k} v^k/k!, where E_{2k} is an Euler number and v = (1/4)*log((1+x)/(1-x)).
EXAMPLE
a(3)=1 because there is one reverse alternating fixed-point-free involution on 1,...,6, viz., 351624.
MATHEMATICA
Table[SeriesCoefficient[(1-x^2)^(-1/4)*(1+x)^(-1/2)*Sum[(-1)^k*EulerE[2*k]*(1/4*Log[(1+x)/(1-x)])^k/k!, {k, 0, n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 29 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Stanley, Jan 22 2006
STATUS
approved