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

0,5

Links

Table of n, a(n) for n=0..23.

Dmitry Efimov, Determinants of generalized binary band matrices, arXiv:1702.05655 [math.RA], 2017.

Formula

a(n) = (A000271(n) + (-1)^n * floor((n-1)/2))/2.

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 *)

Crossrefs

Cf. A000271, A293042.

Sequence in context: A119668 A101538 A045598 * A186860 A139008 A058721

Adjacent sequences: A293040 A293041 A293042 * A293044 A293045 A293046

Keyword

nonn

Author

Eric M. Schmidt, Sep 28 2017

Status

approved