A366775 Number of 2-distant 4-noncrossing partitions of {1,...,n}.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21146, 115938, 677765, 4200011, 27446229, 188255890, 1349652560, 10075332564, 78052115894, 625568350179, 5173033558415, 44028767332852, 384857341649657

Offset: 0

Author

Juan B. Gil, Nov 13 2023

Keywords

• nonn
• more

Comments

a(n+1) is the binomial transform of A108305.

Examples

			There are 21147 partitions of 9 elements, but a(9)=21146 because the partition (1,6)(2,7)(3,8)(4,9)(5) has a 2-distant 4-crossing.
		

References

• Juan B. Gil and Jordan O. Tirrell, A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions, Discrete Math. 343 (2020), no. 6, 111705, 5 pp.

Links

• Juan B. Gil and Jordan O. Tirrell, A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions, arXiv:1806.09065 [math.CO], 2018-2023.

Crossrefs

Cf. A108305, A366774, A366776.

Formula

a(n+1) = Sum_{i=0..n} binomial(n,i)*A108305(i).