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%I #7 Dec 21 2022 21:47:18
%S 1,1,3,9,37,157,811,4309,26327,164947,1151477,8224863,64158567,
%T 511177515,4386520201,38389960685,358214414675,3404632390971,
%U 34234771676473,350261221644771,3768281045014927,41210302324325919,471585931164213345,5480984322433817771,66388136273738685321
%N Number of pairs of partitions (A<=B, that is, A is a refinement of B) of [n] such that A is noncrossing and its nontrivial blocks are of type {a,b} with a <= n and b > n.
%F a(n) = Sum_{k=0..m} binomial(m,k)*binomial(m+e,k)*Bell(n-k), with m = floor(n/2), e = n mod 2 and where Bell(n) is the Bell exponential number A000110(n).
%Y Cf. A000110.
%K nonn
%O 0,3
%A _Francesca Aicardi_, Nov 13 2022
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