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 A374162 #16 Jun 30 2024 11:21:51
%S A374162 1,0,1,2,8,36,198,1272,9384,78240,728040,7482960,84224160,1030569120,
%T A374162 13623366960,193515477120,2939860748160,47568519613440,
%U A374162 816772822750080,14833749363552000,284114908317542400,5723753780712844800,120995656719515424000,2678008828724659584000
%N A374162 a(n) is the number of permutations of size n ending with n whose n left-to-right maxima are consecutive and nonadjacent.
%H A374162 Lapo Cioni, Luca Ferrari, and Rebecca Smith, <a href="https://arxiv.org/abs/2406.16399">Pop Stacks with a Bypass</a>, arXiv:2406.16399 [cs.DM], 2024. See p. 76.
%F A374162 a(1) = 1 and a(n) = Sum_{k=2..ceiling(n/2)} (n-k)!*binomial(n-k-1, k-2) for n > 1.
%t A374162 a[1]=1; a[n_]:=Sum[(n-k)!Binomial[n-k-1,k-2],{k,2,Ceiling[n/2]}]; Array[a,24]
%Y A374162 Cf. A119502, A374165.
%K A374162 nonn
%O A374162 1,4
%A A374162 _Stefano Spezia_, Jun 30 2024