A366776 Number of 2-distant 5-noncrossing partitions of {1,...,n}.

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213546, 27642948, 190866373, 1382340849, 10469739750, 82701857286, 679644668584, 5797647603036, 51228938289039, 467980667203765

Offset: 0

Author

Juan B. Gil, Nov 13 2023

Keywords

• nonn
• more

Comments

a(n+1) is the binomial transform of A192126.

Examples

			There are 678570 partitions of 11 elements, but a(11)=678569 because the partition (1,7)(2,8)(3,9)(4,10)(5,11)(6) has a 2-distant 5-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. A192126, A366774, A366775.

Formula

a(n+1) = Sum_{i=0..n} binomial(n,i)*A192126(i).