A293043 Number of odd permutations p of {1,...,n} such that p(i) is not i or i+1.
0, 0, 0, 0, 2, 7, 49, 336, 2708, 24398, 244298, 2689664, 32297990, 420096141, 5883813379, 88287031264, 1412982765800, 24026200566396, 432554403678612, 8219863859175936, 164419973194802826, 3453229295483253843, 75978854506098366005, 1747670263607990439472
Offset: 0
Keywords
Links
- Dmitry Efimov, Determinants of generalized binary band matrices, arXiv:1702.05655 [math.RA], 2017.
Programs
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Mathematica
a[n_] := (Sum[(-1)^(n-k) k! Binomial[n+k, 2 k], {k, 0, n}] + (-1)^n* Floor[(n - 1)/2])/2; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Feb 18 2019 *)
Formula
a(n) = (A000271(n) + (-1)^n * floor((n-1)/2))/2.