

A362172


a(n) = the hypergraph Catalan number C_7(n).


9




OFFSET

0,3


COMMENTS

Let m >= 1. The sequence of hypergraph Catalan numbers {C_m(n): n >= 0} is defined in terms of counting walks on trees, weighted by the orders of their automorphism groups. See Gunnells. When m = 1 we get the sequence of Catalan numbers A000108. The present sequence is the case m = 7.
Gunnells gives several combinatorial interpretations of the hypergraph Catalan numbers, a method to compute their generating functions to arbitrary precision and some conjectural asymptotics.


LINKS



FORMULA

a(n) ~ sqrt(7)/4 * (7^6/6!)^n * n!^6/(Pi*n)^3 (conjectural).


CROSSREFS



KEYWORD

nonn,walk,more


AUTHOR



STATUS

approved



