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 A167995 #45 Jul 05 2024 11:11:01
%S A167995 1,1,3,10,44,238,1506,10960,90449,834166,8496388,94738095,1148207875,
%T A167995 15031585103,211388932628
%N A167995 Total number of permutations on {1,2,...,n} that have a unique longest increasing subsequence.
%H A167995 Miklos Bona and Elijah DeJonge, <a href="https://arxiv.org/abs/2003.10640">Pattern avoiding permutations and involutions with a unique longest increasing subsequence</a>, arXiv:2003.10640 [math.CO], 2020.
%H A167995 Manfred Scheucher, <a href="/A167995/a167995.c.txt">C Code</a>
%H A167995 Nicholas Van Nimwegen, <a href="https://arxiv.org/abs/2303.02808">A Combinatorial Proof for 132-Avoiding Permutations with a Unique Longest Increasing Subsequence</a>, arXiv:2303.02808 [math.CO], 2023. Mentions this sequence.
%H A167995 Nicholas Van Nimwegen, <a href="https://ajc.maths.uq.edu.au/pdf/89/ajc_v89_p397.pdf">Unique longest increasing subsequences in 132-avoiding permutations</a>, Australasian J. Comb. (2024) Vol. 89, Part 3. 397-399.
%e A167995 For n=3, 123, 231, and 312 are the only three permutations that have precisely one maximal increasing subsequence.
%e A167995 The permutation 35142678 has longest increasing subsequence length 5, but this maximal length can be obtained in multiple ways (35678, 34678, 14678, 12678), hence it is not counted in a(8). - _Bert Dobbelaere_, Jul 24 2019
%o A167995 (Sage)
%o A167995 print(n,len([p for p in permutations(n) if len(p.longest_increasing_subsequences())==1]))
%o A167995 # _Manfred Scheucher_, Jun 06 2015
%Y A167995 Cf. A167999, A168502.
%K A167995 nonn,nice,more
%O A167995 1,3
%A A167995 _Anant Godbole_, Stephanie Goins, Brad Wild, Nov 16 2009
%E A167995 a(9)-a(13) from _Manfred Scheucher_, Jun 06 2015
%E A167995 a(14)-a(15) from _Bert Dobbelaere_, Jul 24 2019