A293042 Number of even permutations p of {1,...,n} such that p(i) is not i or i+1.
1, 0, 0, 1, 1, 9, 47, 339, 2705, 24402, 244294, 2689669, 32297985, 420096147, 5883813373, 88287031271, 1412982765793, 24026200566404, 432554403678604, 8219863859175945, 164419973194802817, 3453229295483253853, 75978854506098365995, 1747670263607990439483
Offset: 0
Keywords
Links
- Dmitry Efimov, Determinants of generalized binary band matrices, arXiv:1702.05655 [math.RA], 2017.
Programs
-
Mathematica
a[n_] := (Sum[(-1)^(n-k) k! Binomial[n+k, 2 k], {k, 0, n}] + (-1)^(n-1)* Floor[(n-1)/2])/2; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Feb 18 2019 *)
Formula
a(n) = (A000271(n) + (-1)^(n-1) * floor((n-1)/2))/2.