

A362169


a(n) = the hypergraph Catalan number C_4(n).


5




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 = 4.
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(2) * (32/3)^n * n!^3/(Pi*n)^(3/2) (conjectural).


CROSSREFS



KEYWORD

nonn,walk,more


AUTHOR



STATUS

approved



