A153743 Number of elements in wreath product C_4 wr S_n that alternate up/not-up with respect to a weak product ordering.

4, 10, 100, 565, 9356, 79584, 1844492, 20922625, 623457040, 8840131486, 321957866768, 5478133336309, 235789017471008, 4680625831294820, 232457094647793632, 5273696164520751265, 296832635265929103616

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

Sequence in context: A203179 A125855 A261842 * A370987 A245304 A298953

Adjacent sequences: A153740 A153741 A153742 * A153744 A153745 A153746

Keyword

nonn

Author

Andrew Niedermaier, Dec 31 2008

Status

approved