A273996 Number of endofunctions on [n] whose cycle lengths are factorials.

1, 1, 4, 25, 218, 2451, 33952, 560407, 10750140, 235118665, 5775676496, 157448312649, 4716609543736, 154007821275595, 5443783515005760, 207093963680817511, 8436365861409555728, 366403740283162634193, 16900793597898691865920, 825115046704241167668025

Offset

0,3

Links

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

Maple

b:= proc(n) option remember; local r, f, g;
      if n=0 then 1 else r, f, g:= $0..2;
      while f<=n do r:= r+(f-1)!*b(n-f)*
         binomial(n-1, f-1); f, g:= f*g, g+1
      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, f, g}, If[n == 0, 1, {r, f, g} = {0, 1, 2}; While[f <= n, r = r + (f - 1)!*b[n - f]*Binomial[n - 1, f - 1]; {f, g} = {f*g, g + 1}]; 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. A000142, A060435, A116956, A272603, A273994, A273997, A273998, A305824.

Sequence in context: A060911 A060912 A209319 * A246530 A268163 A050386

Adjacent sequences: A273993 A273994 A273995 * A273997 A273998 A273999

Keyword

nonn

Author

Alois P. Heinz, Jun 06 2016

Status

approved