A362217 a(n) = the hypergraph Fuss-Catalan number FC_(3,3)(n).

1, 1, 38440, 8272793255000, 9396808005460764741084000

Offset: 0

Author

Peter Bala, Apr 11 2023

Keywords

• nonn
• walk
• more

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

Cf. A000108, A355262, A362167, A362214, A362215, A362216.