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 A363449 #61 Jul 21 2024 19:58:14
%S A363449 0,0,1,1,5,16,55,197,705,2563,9381,34563,128029,476347,1779107,
%T A363449 6666752,25054585,94401460,356510371,1349182629,5115555725,
%U A363449 19429832443,73916249353,281613780638,1074400168957,4104279704526,15697542046005,60106182177517,230394256650275,884024296630081,3395269379129779
%N A363449 Number of noncrossing partitions of the n-set with some pair of singletons {i} and {j} that can be merged into {i,j} and leave the partition a noncrossing-partition.
%C A363449 a(n) is the number of non-maximal sets of noncrossing lanes in a road intersection where U-turns are forbidden and where n entries and n exits are alternated.
%H A363449 Julien Rouyer, <a href="/A363449/b363449.txt">Table of n, a(n) for n = 0..87</a>
%H A363449 Julien Rouyer and A. Ninet, <a href="https://hal.science/hal-04281025">Two New Integer Sequences Related to Crossroads and Catalan Numbers</a>, hal-04281025, 2023. See also <a href="https://arxiv.org/abs/2311.07181">arXiv:2311.07181</a> [math.CO], 2023.
%F A363449 a(n) = A000108(n) - A363448(n).
%e A363449 The 5 noncrossing partitions of the 4-set {1234} with some pair of singletons that can be merged and leave the partition a noncrossing-partition are [{1},{2},{3},{4}], [{12},{3},{4}], [{1},{23},{4}], [{2},{3},{14}], [{1},{2},{34}].
%e A363449 [{1},{23},{4}] can give [{14},{23}].
%Y A363449 Difference between A000108 and A363448.
%K A363449 nonn,hard
%O A363449 0,5
%A A363449 _Julien Rouyer_, Jun 02 2023
%E A363449 Extended by _Julien Rouyer_, Apr 23 2024