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A272640 Number of permutations of [1..n] which achieve the worse case bound for a graph domination problem. 2
1, 1, 2, 4, 24, 56, 640, 1632, 30464, 81664, 2251008, 6241280, 238222336, 676506624, 34141233152, 98709925888, 6363055718400, 18655203885056, 1495281327013888, 4432984678858752, 432399526939590656, 1293646660855398400, 150872297033214984192 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 18 09:53 EST 2019. Contains 329261 sequences. (Running on oeis4.)