A362215 a(n) = the hypergraph Fuss-Catalan number FC_(2,3)(n).

1, 1, 480, 200225, 18527520, 45589896150400

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) = (2,3).

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

Table of n, a(n) for n=0..5.

Parth Chavan, Andrew Lee and Karthik Seetharaman, Hypergraph Fuss-Catalan numbers, arXiv:2202.01111 [math.CO], 2022.

Crossrefs

Cf. A000108, A355262, A362167, A362214, A362216, A362217.

Sequence in context: A289638 A289744 A287933 * A304395 A269759 A317174

Adjacent sequences: A362212 A362213 A362214 * A362216 A362217 A362218

Keyword

nonn,walk,more

Author

Peter Bala, Apr 11 2023

Status

approved