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A362217
a(n) = the hypergraph Fuss-Catalan number FC_(3,3)(n).
3
1, 1, 38440, 8272793255000, 9396808005460764741084000
OFFSET
0,3
COMMENTS
Chavan et al. associate to each pair (r,m) of positive integers the sequence of hypergraph Fuss-Catalan numbers {FC_(r,m)(n) : n >= 0}. This is the case (r,m) = (3,3).
When m = 1, the sequence {FC_(r,1)(n) : n >= 0} is equivalent to the sequence of Fuss-Catalan numbers { (1/(r*n+1))*binomial((r+1)*n,n) : n >= 0}. Note that r = 1 corresponds to the Catalan numbers A000108. See A355262 for a table of Fuss-Catalan numbers.
When r = 1, the sequence {FC_(1,m)(n) : n >= 0} is equivalent to the sequence of hypergraph Catalan numbers {C_m(n) : n >= 0}. See A362167 - A362172 for the cases m = 2 through 7.
LINKS
Parth Chavan, Andrew Lee and Karthik Seetharaman, Hypergraph Fuss-Catalan numbers, arXiv:2202.01111 [math.CO], 2022.
CROSSREFS
KEYWORD
nonn,walk,more
AUTHOR
Peter Bala, Apr 11 2023
STATUS
approved