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 A258683 #20 Mar 07 2020 12:39:00
%S A258683 1,0,0,0,2,16,120,938,8014,74060,748628,8163156,96429784
%N A258683 Total number of permutations on {1,2,...,n} that have a unique longest increasing subsequence and a unique longest decreasing subsequence.
%C A258683 By definition, a(n) <= A167995(n).
%H A258683 Manfred Scheucher, <a href="/A258683/a258683.c.txt">C Code</a>
%e A258683 the two permutation of {1,2,...,5}:
%e A258683 {2, 5, 3, 1, 4}
%e A258683 {4, 1, 3, 5, 2}
%e A258683 8 of the 16 permutations of {1,2,...,6} (others reversed):
%e A258683 {1, 3, 6, 4, 2, 5}
%e A258683 {1, 5, 2, 4, 6, 3}
%e A258683 {2, 3, 6, 4, 1, 5}
%e A258683 {2, 5, 3, 1, 4, 6}
%e A258683 {2, 6, 3, 1, 4, 5}
%e A258683 {2, 6, 5, 3, 1, 4}
%e A258683 {3, 6, 4, 2, 1, 5}
%e A258683 {3, 6, 4, 2, 5, 1}
%o A258683 (Sage)
%o A258683 def A258683(n):
%o A258683 return len([p for p in permutations(n) if len(p.longest_increasing_subsequences())* len(p.reverse().longest_increasing_subsequences())==1])
%o A258683 # _Manfred Scheucher_, Jun 07 2015
%Y A258683 Cf. A167995, A167999, A168502.
%K A258683 nonn,more
%O A258683 1,5
%A A258683 _Manfred Scheucher_, Jun 07 2015