A272640 Number of permutations of [1..n] which achieve the worse case bound for a graph domination problem.

1, 1, 2, 4, 24, 56, 640, 1632, 30464, 81664, 2251008, 6241280, 238222336, 676506624, 34141233152, 98709925888, 6363055718400, 18655203885056, 1495281327013888, 4432984678858752, 432399526939590656, 1293646660855398400, 150872297033214984192

Offset

0,3

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..200

C. Coscia, J. DeWitt, F. Yang, Y. Zhang, Online and Random Domination of Graphs, arXiv preprint arXiv:1509.08876 [math.CO], 2015.

Jonathan Dewitt, Christopher Coscia, Fan Yang, Yiguang Zhang, Best and Worst Case Permutations for Random Online Domination of the Path, Discrete Mathematics & Theoretical Computer Science, December 20, 2017, Vol. 19 no. 2, Permutation Patterns 2016.

Formula

Propositions 3.2 and 3.4 of Coscia et al. 2015 give formulas.

E.g.f.: sinh(x)/(cosh(x) - x*sinh(x)) + 1/(cosh(x) - x*sinh(x))^2 (see Theorem 3.5 of Coscia et al. 2015). - Gheorghe Coserea, May 12 2016

Mathematica

terms = 23; egf = Sinh[x]/(Cosh[x] - x Sinh[x]) + 1/(Cosh[x] - x Sinh[x])^2 + O[x]^terms; CoefficientList[egf, x] Range[0, terms-1]! (* Jean-François Alcover, Sep 06 2018, after Gheorghe Coserea *)

Prog

(PARI) x = 'x + O('x^23);
Vec(serlaplace(sinh(x)/(cosh(x) - x*sinh(x)) + 1/(cosh(x) - x*sinh(x))^2)) \\ Gheorghe Coserea, May 12 2016

Crossrefs

Cf. A113583, A272641.

Sequence in context: A168054 A280075 A068506 * A192513 A192384 A119036

Adjacent sequences: A272637 A272638 A272639 * A272641 A272642 A272643

Keyword

nonn

Author

N. J. A. Sloane, May 06 2016

Extensions

More terms from Gheorghe Coserea, May 12 2016

Status

approved