A374162 a(n) is the number of permutations of size n ending with n whose n left-to-right maxima are consecutive and nonadjacent.
1, 0, 1, 2, 8, 36, 198, 1272, 9384, 78240, 728040, 7482960, 84224160, 1030569120, 13623366960, 193515477120, 2939860748160, 47568519613440, 816772822750080, 14833749363552000, 284114908317542400, 5723753780712844800, 120995656719515424000, 2678008828724659584000
Offset: 1
Keywords
Links
- Lapo Cioni, Luca Ferrari, and Rebecca Smith, Pop Stacks with a Bypass, arXiv:2406.16399 [cs.DM], 2024. See p. 76.
Programs
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Mathematica
a[1]=1; a[n_]:=Sum[(n-k)!Binomial[n-k-1,k-2],{k,2,Ceiling[n/2]}]; Array[a,24]
Formula
a(1) = 1 and a(n) = Sum_{k=2..ceiling(n/2)} (n-k)!*binomial(n-k-1, k-2) for n > 1.