A362216 a(n) = the hypergraph Fuss-Catalan number FC_(3,2)(n).

1, 1, 11532, 628958939250, 163980917165716725552156

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) = (3,2).

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..4.

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

Crossrefs

Cf. A000108, A355262, A362167, A362214, A362215, A362217.

Sequence in context: A235659 A258564 A258561 * A063061 A237304 A292039

Adjacent sequences: A362213 A362214 A362215 * A362217 A362218 A362219

Keyword

nonn,walk,more

Author

Peter Bala, Apr 11 2023

Status

approved