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%I #20 Nov 18 2023 08:36:28
%S 1,1,2,5,15,52,203,877,4140,21146,115938,677765,4200011,27446229,
%T 188255890,1349652560,10075332564,78052115894,625568350179,
%U 5173033558415,44028767332852,384857341649657
%N Number of 2-distant 4-noncrossing partitions of {1,...,n}.
%C a(n+1) is the binomial transform of A108305.
%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)*A108305(i).
%e 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.
%Y Cf. A108305, A366774, A366776.
%K nonn,more
%O 0,3
%A _Juan B. Gil_, Nov 13 2023