The On-Line Encyclopedia of Integer Sequences (OEIS)

A366776 revision #14

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

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OFFSET

0,3

COMMENTS

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

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)*A192126(i).

EXAMPLE

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.

CROSSREFS

Cf. A192126, A366774, A366775.

Sequence in context: A287259 A287671 A164864 * A192866 A229227 A287589

Adjacent sequences: A366773 A366774 A366775 * A366777 A366778 A366779

KEYWORD

nonn,changed

AUTHOR

Juan B. Gil, Nov 13 2023

STATUS

reviewed