A078509 Number of permutations p of {1,2,...,n} such that p(i)-i != 1 and p(i)-i != 2 for all i.

1, 1, 1, 1, 5, 23, 131, 883, 6859, 60301, 591605, 6405317, 75843233, 974763571, 13512607303, 200949508327, 3190881283415, 53880906258521, 964039575154409, 18217997734199113, 362584510633666621, 7580578211464070863, 166099466140519353035, 3806162403831340850651

Offset: 0

Author

Vladimir Baltic, Vladeta Jovovic, Jan 05 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A000255, A055790, A001883, A001887, A075851, A075852.

Programs

Maple

a:= proc(n) option remember; `if`(n<4, 1,
      (n-1)*a(n-1) +(n-3)*a(n-2) +a(n-3))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jan 10 2014

Mathematica

a = DifferenceRoot[Function[{y, n}, {-y[n] - n y[n+1] - (n+2) y[n+2] + y[n+3] == 0, y[0] == 1, y[1] == 1, y[2] == 1, y[3] == 1}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *)

Formula

From Vladeta Jovovic, Jul 16 2007: (Start)

G.f.: x/(1+x)*Sum_{n>=0} (n+1)!*(x/(1+x)^2)^n.

a(n) = Sum_{k=1..n} (-1)^(n-k)*k!*binomial(n+k-2,2*k-2). (End)

a(n) ~ exp(-2) * n!. - Vaclav Kotesovec, Aug 25 2014

Extensions

More terms from Alois P. Heinz, Jan 10 2014