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A329944 Number of permutations of [n] whose cycle lengths avoid primes. 4
1, 1, 1, 1, 7, 31, 211, 1051, 10081, 107857, 1227241, 8969401, 108817831, 1173362191, 19426473067, 320062090531, 5692838161921, 70426164947041, 1346222143950481, 21952313047471537, 493701484264143751, 10971915198235355071, 266542798822750395331 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
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
Sequence in context: A223144 A155521 A201116 * A060015 A261558 A241456
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 24 2019
STATUS
approved

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Last modified April 16 20:32 EDT 2024. Contains 371754 sequences. (Running on oeis4.)