A363449 Number of noncrossing partitions of the n-set with some pair of singletons {i} and {j} that can be merged into {i,j} and leave the partition a noncrossing-partition.

0, 0, 1, 1, 5, 16, 55, 197, 705, 2563, 9381, 34563, 128029, 476347, 1779107, 6666752, 25054585, 94401460, 356510371, 1349182629, 5115555725, 19429832443, 73916249353, 281613780638, 1074400168957, 4104279704526, 15697542046005, 60106182177517, 230394256650275, 884024296630081, 3395269379129779

Offset: 0

Author

Julien Rouyer, Jun 02 2023

Keywords

• nonn
• hard

Comments

a(n) is the number of non-maximal sets of noncrossing lanes in a road intersection where U-turns are forbidden and where n entries and n exits are alternated.

Examples

			The 5 noncrossing partitions of the 4-set {1234} with some pair of singletons that can be merged and leave the partition a noncrossing-partition are [{1},{2},{3},{4}], [{12},{3},{4}], [{1},{23},{4}], [{2},{3},{14}], [{1},{2},{34}].
[{1},{23},{4}] can give [{14},{23}].
		

Links

• Julien Rouyer, Table of n, a(n) for n = 0..87
• Julien Rouyer and A. Ninet, Two New Integer Sequences Related to Crossroads and Catalan Numbers, hal-04281025, 2023. See also arXiv:2311.07181 [math.CO], 2023.

Crossrefs

Difference between A000108 and A363448.

Formula

a(n) = A000108(n) - A363448(n).

Extensions

Extended by Julien Rouyer, Apr 23 2024