OFFSET
0,3
COMMENTS
A pair (C,O) is a surjective compatible pair if O is an acyclic orientation of the edges of a simple labeled graph G on n nodes, and C is a surjective function from V(G)->{1,2,...k} for some positive integer k such that for all u,v in V(G) if u->v under the orientation then C(u)>= C(v).
LINKS
R. P. Stanley, Acyclic orientation of graphs, Discrete Math. 5 (1973), 171-178.
FORMULA
Let E(x) = Sum_{n>=0}x^n/(n! 2^Binomial(n,2)). Then Sum_{n>=0}a_n x^n/(n! 2^Binomial(n,2)) = 1/(2 - E(-x)^-1).
MATHEMATICA
nn = 12; b[n_] := q^Binomial[n, 2] n! /. q -> 2; e[z_] := Sum[z^n/b[n], {n, 0, nn}]; Table[b[n], {n, 0, nn}] CoefficientList[ Series[1/(1 - (1/e[-z] - 1)), {z, 0, nn}], z]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Feb 28 2021
STATUS
approved