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 A273998 Number of endofunctions on [n] whose cycle lengths are primes. 6
 1, 0, 1, 8, 75, 904, 13255, 229536, 4587961, 103971680, 2634212961, 73787255200, 2264440519891, 75563445303072, 2724356214102055, 105546202276277504, 4373078169296869425, 192970687573630633216, 9035613818754820178689, 447469496697658409400960 (list; graph; refs; listen; history; text; internal format)
 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: A067306 A261065 A071720 * A111685 A302814 A088376 Adjacent sequences:  A273995 A273996 A273997 * A273999 A274000 A274001 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 06 2016 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)