A247978 Number of permutations of [n] that have no prime fixed points.

1, 1, 1, 3, 14, 64, 426, 2790, 24024, 229080, 2399760, 25022880, 312273360, 3884393520, 56255149440, 869007242880, 14266826784000, 233845982899200, 4309095479673600, 79300508301907200, 1620482929875532800, 34699018357638835200, 777011144137311283200

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Formula

a(n) = Sum_{j=0..pi(n)} (-1)^(j)*C(pi(n),j)*(n-j)!, with pi = A000720.

Example

a(2) = 1: 21.
a(3) = 3: 132, 231, 312.
a(4) = 14: 1324, 1342, 1423, 2143, 2314, 2341, 2413, 3124, 3142, 3412, 3421, 4123, 4312, 4321.

Maple

with(numtheory):
a:= n-> add((-1)^(j)*binomial(pi(n), j)*(n-j)!, j=0..pi(n)):
seq(a(n), n=0..25);

Mathematica

a[n_] := Sum[(-1)^j*Binomial[PrimePi[n], j]*(n-j)!, {j, 0, PrimePi[n]}]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 26 2017, translated from Maple *)

Prog

(PARI) for(n=0, 25, print1(sum(j=0, primepi(n), (-1)^j*binomial(primepi(n), j)*(n - j)!), ", ")) \\ Indranil Ghosh, Mar 08 2017

Crossrefs

Cf. A000720, A161131, A161132, A187847.

Sequence in context: A151239 A151240 A161131 * A026592 A034275 A240008

Adjacent sequences: A247975 A247976 A247977 * A247979 A247980 A247981

Keyword

nonn

Author

Alois P. Heinz, Nov 02 2014

Status

approved