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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
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
1,4
LINKS
Lapo Cioni, Luca Ferrari, and Rebecca Smith, Pop Stacks with a Bypass, arXiv:2406.16399 [cs.DM], 2024. See p. 76.
FORMULA
a(1) = 1 and a(n) = Sum_{k=2..ceiling(n/2)} (n-k)!*binomial(n-k-1, k-2) for n > 1.
MATHEMATICA
a[1]=1; a[n_]:=Sum[(n-k)!Binomial[n-k-1, k-2], {k, 2, Ceiling[n/2]}]; Array[a, 24]
CROSSREFS
Sequence in context: A052582 A367920 A222468 * A020021 A213076 A233744
KEYWORD
nonn
AUTHOR
Stefano Spezia, Jun 30 2024
STATUS
approved