OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..400
A. Niedermaier and J. Remmel, Analogues of Up-down Permutations for Colored Permutations, J. Int. Seq. 13 (2010), 10.5.6.
FORMULA
E.g.f.: (6 + 6*sin(x) + 18*x*cos(x) - 9*x^2*sin(x) - x^3*cos(x)) / (6*cos(x) - 18*x*sin(x) - 9*x^2*cos(x) + x^3*sin(x)).
EXAMPLE
Viewing elements in one-line notation as a list of ordered pairs with first entries in [4] and second entries forming a permutation in S_n, two of the 100 up/not-up elements for n=3 are (1,2) (4,3) (3,1) and (1,1) (1,3) (4,2). Note that the first element goes up/down and the second goes up/not-up with respect to the weak product ordering on ordered pairs.
MATHEMATICA
Rest[CoefficientList[Series[(6 + 6*Sin[x] + 18*x*Cos[x] - 9 x^2*Sin[x] - x^3*Cos[x])/(6*Cos[x] - 18*x*Sin[x] - 9 x^2*Cos[x] + x^3*Sin[x]), {x, 0, 40}], x]*Range[0, 40]!] (* G. C. Greubel, Aug 27 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Niedermaier, Dec 31 2008
STATUS
approved