A361529 Number of noncrossing partitions of an n-set with distinct block sizes.

1, 1, 1, 4, 5, 11, 43, 64, 137, 253, 1121, 1596, 3625, 6475, 12825, 51766, 77393, 163609, 299719, 577126, 980581, 4105291, 5770601, 12332486, 21758449, 41755501, 69558113, 127657648, 466063781, 669034815, 1357587571, 2383561636, 4432375521, 7377464689, 13211074817, 21284795176, 76820589073

Offset

0,4

Comments

It appears that a(n) = a(n+4) mod 2 and a(n) = a(n+18) mod 3.

Links

Table of n, a(n) for n=0..36.

Example

For n = 3, the noncrossing partitions of {1,2,3} are:
  {1,2,3}
  {1,2},{3}
  {1,3},{2}
  {1},{2,3}
  {1},{2},{3}
Four of these have distinct block sizes so a(3) = 4.

Crossrefs

Cf. A000108 (noncrossing partitions), A007837.

Sequence in context: A304224 A304135 A251240 * A305041 A316731 A253086

Adjacent sequences: A361526 A361527 A361528 * A361530 A361531 A361532

Keyword

nonn

Author

Peter Kildeager, Mar 14 2023

Extensions

Terms corrected by Peter Kildeager, Jan 18 2024

Status

approved