This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358397 #7 Dec 21 2022 21:47:18
%S A358397 1,1,3,9,37,157,811,4309,26327,164947,1151477,8224863,64158567,
%T A358397 511177515,4386520201,38389960685,358214414675,3404632390971,
%U A358397 34234771676473,350261221644771,3768281045014927,41210302324325919,471585931164213345,5480984322433817771,66388136273738685321
%N A358397 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 A358397 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 A358397 Cf. A000110.
%K A358397 nonn
%O A358397 0,3
%A A358397 _Francesca Aicardi_, Nov 13 2022