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

0,3

Comments

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

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

Table of n, a(n) for n=0..21.

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.

Formula

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

Example

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.

Crossrefs

Cf. A108305, A366774, A366776.

Sequence in context: A287257 A287669 A099263 * A192865 A229225 A343669

Adjacent sequences: A366772 A366773 A366774 * A366776 A366777 A366778

Keyword

nonn,more

Author

Juan B. Gil, Nov 13 2023

Status

approved