A329944 Number of permutations of [n] whose cycle lengths avoid primes.

1, 1, 1, 1, 7, 31, 211, 1051, 10081, 107857, 1227241, 8969401, 108817831, 1173362191, 19426473067, 320062090531, 5692838161921, 70426164947041, 1346222143950481, 21952313047471537, 493701484264143751, 10971915198235355071, 266542798822750395331

Offset

0,5

Links

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

Formula

a(n) mod 2 = 1.

a(n) mod 10 = period 5: repeat [1,1,1,1,7], g.f.: (7*x^4+x^3+x^2+x+1)/(1-x^5).

Example

a(4) = 7: (1)(2)(3)(4), (1234), (1243), (1324), (1342), (1423), (1432).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(`if`(isprime(j), 0,
      a(n-j)*binomial(n-1, j-1)*(j-1)!), j=1..n))
    end:
seq(a(n), n=0..25);

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[If[PrimeQ[j], 0,
     a[n-j] Binomial[n-1, j-1] (j-1)!], {j, 1, n}]];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Oct 31 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A218002, A329945, A364450.

Sequence in context: A223144 A155521 A201116 * A060015 A261558 A241456

Adjacent sequences: A329941 A329942 A329943 * A329945 A329946 A329947

Keyword

nonn

Author

Alois P. Heinz, Nov 24 2019

Status

approved