A291111 Number of endofunctions on [n] such that the LCM of their cycle lengths equals five.

0, 0, 0, 0, 0, 24, 864, 24192, 653184, 18144000, 531365184, 16563076992, 551172885120, 19580825392128, 741547690884000, 29873618711000064, 1277121733631347968, 57795924098354577408, 2762004604309125452928, 139058300756829929472000, 7359536118308288021017344

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..387

Formula

a(n) ~ (2*exp(6/5)-exp(1)) * n^(n-1). - Vaclav Kotesovec, Aug 18 2017

Maple

b:= proc(n, m) option remember; (k-> `if`(m>k, 0,
      `if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))
       *binomial(n-1, j-1)*(j-1)!, j=1..n))))(5)
    end:
a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..22);

Mathematica

b[n_, m_] := b[n, m] = With[{k = 5}, If[m > k, 0, If[n == 0, If[m == k, 1, 0], Sum[b[n-j, LCM[m, j]] Binomial[n-1, j-1] (j-1)!, {j, 1, n}]]]];
a[n_] := If[n == 0, 0, Sum[b[j, 1] n^(n-j) Binomial[n-1, j-1], {j, 0, n}]];
a /@ Range[0, 22] (* Jean-François Alcover, Dec 29 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A222029.

Sequence in context: A220176 A275563 A275088 * A246215 A109575 A160111

Adjacent sequences: A291108 A291109 A291110 * A291112 A291113 A291114

Keyword

nonn

Author

Alois P. Heinz, Aug 17 2017

Status

approved