%I #18 Nov 18 2023 08:36:41

%S 1,1,2,5,15,52,203,877,4140,21147,115975,678569,4213546,27642948,

%T 190866373,1382340849,10469739750,82701857286,679644668584,

%U 5797647603036,51228938289039,467980667203765

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

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

%D 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.

%H Juan B. Gil and Jordan O. Tirrell, <a href="https://arxiv.org/abs/1806.09065">A simple bijection for enhanced, classical, and 2-distant k-noncrossing partitions</a>, arXiv:1806.09065 [math.CO], 2018-2023.

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

%e 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.

%Y Cf. A192126, A366774, A366775.

%K nonn,more

%O 0,3

%A _Juan B. Gil_, Nov 13 2023