A277493 - OEIS

%I #38 Dec 11 2016 06:55:20

%S 1,2,10,66,504,4216,37548,350090,3380520,33558024,340670720,

%T 3522993656,37003723200,393856445664,4240313009272,46109094112170

%N Number of planar rooted Eulerian orientations (i.e., planar directed Eulerian maps with in-degree and out-degree equal for each vertex) with n edges.

%C a(n) is the coefficient of t^n in the generating function O(t) = sum_w O_w(t), where w is any binary word on the alphabet {0,1} having as many 0's as 1's.

%C The series O_w(t) are defined by O_epsilon(t) = 1 (for the empty word epsilon) and O_w(t) = t* sum_{w=aubv} O_u(t)*O_v(t) + t* sum_u O_uw'(t), where: a is a binary letter (0 or 1), b = 1-a, w' is the suffix of w of length |w|-1.

%H Nicolas Bonichon, Mireille Bousquet-Mélou, Paul Dorbec, and Claire Pennarun, <a href="https://hal.archives-ouvertes.fr/hal-01389264">On the number of planar Eulerian orientations</a>, HAL preprint <hal-01389264> [math.CO], 2016

%H Nicolas Bonichon, Mireille Bousquet-Mélou, Paul Dorbec, Claire Pennarun, <a href="https://arxiv.org/abs/1610.09837">On the number of planar Eulerian orientations</a>, arXiv:1610.09837 [math.CO], 2016

%H Claire Pennarun, <a href="http://www.labri.fr/perso/cpennaru/PeoGeneration.cpp">A C++ program generating the sequence</a>

%K nonn,more

%O 0,2

%A _Claire Pennarun_, Oct 17 2016