A273998 Number of endofunctions on [n] whose cycle lengths are primes.

1, 0, 1, 8, 75, 904, 13255, 229536, 4587961, 103971680, 2634212961, 73787255200, 2264440519891, 75563445303072, 2724356214102055, 105546202276277504, 4373078169296869425, 192970687573630633216, 9035613818754820178689, 447469496697658409400960

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..386

Maple

b:= proc(n) option remember; local r, p;
      if n=0 then 1 else r, p:=0, 2;
      while p<=n do r:= r+(p-1)!*b(n-p)*
         binomial(n-1, p-1); p:= nextprime(p)
      od; r fi
    end:
a:= n-> add(b(j)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..20);

Mathematica

b[n_] := b[n] = Module[{r, p}, If[n == 0, 1, {r, p} = {0, 2}; While[p <= n, r = r + (p - 1)!*b[n - p]*Binomial[n-1, p-1]; p = NextPrime[p]]; r]];
a[0] = 1; a[n_] := Sum[b[j]*n^(n - j)*Binomial[n - 1, j - 1], {j, 0, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jun 06 2018, from Maple *)

Crossrefs

Cf. A000040, A060435, A116956, A218002, A273994, A273996, A273997, A305824.

Sequence in context: A361528 A261065 A071720 * A111685 A302814 A088376

Adjacent sequences: A273995 A273996 A273997 * A273999 A274000 A274001

Keyword

nonn

Author

Alois P. Heinz, Jun 06 2016

Status

approved