A272640 - OEIS

%I #29 Sep 06 2018 09:09:12

%S 1,1,2,4,24,56,640,1632,30464,81664,2251008,6241280,238222336,

%T 676506624,34141233152,98709925888,6363055718400,18655203885056,

%U 1495281327013888,4432984678858752,432399526939590656,1293646660855398400,150872297033214984192

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

%H Gheorghe Coserea, <a href="/A272640/b272640.txt">Table of n, a(n) for n = 0..200</a>

%H C. Coscia, J. DeWitt, F. Yang, Y. Zhang, <a href="http://arxiv.org/abs/1509.08876">Online and Random Domination of Graphs</a>, arXiv preprint arXiv:1509.08876 [math.CO], 2015.

%H Jonathan Dewitt, Christopher Coscia, Fan Yang, Yiguang Zhang, <a href="https://dmtcs.episciences.org/4145">Best and Worst Case Permutations for Random Online Domination of the Path</a>, Discrete Mathematics & Theoretical Computer Science, December 20, 2017, Vol. 19 no. 2, Permutation Patterns 2016.

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

%F 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

%t 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_ *)

%o (PARI) x = 'x + O('x^23);

%o Vec(serlaplace(sinh(x)/(cosh(x) - x*sinh(x)) + 1/(cosh(x) - x*sinh(x))^2)) \\ _Gheorghe Coserea_, May 12 2016

%Y Cf. A113583, A272641.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, May 06 2016

%E More terms from _Gheorghe Coserea_, May 12 2016