A246192 Number of endofunctions on [n] where the smallest cycle length equals 5.

24, 720, 17640, 430080, 11022480, 302472576, 8937981360, 284552040960, 9743091569640, 357820740076800, 14051646110285784, 588177615908413440, 26161789829441054880, 1232890909824506204160, 61387038018996808785120, 3221070809733138102829056

Offset

5,1

Links

Alois P. Heinz, Table of n, a(n) for n = 5..200

Formula

a(n) ~ (exp(-25/12) - exp(-137/60)) * n^n. - Vaclav Kotesovec, Aug 21 2014

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
      add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
      b(n-i*j, i+1), j=0..n/i)))
    end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
a:= n-> A(n, 5) -A(n, 6):
seq(a(n), n=5..25);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n==0, 1, If[i>n, 0, Sum[(i - 1)!^j multinomial[n, Join[{n - i*j}, Table[i, {j}]]]/j! b[n - i*j, i + 1], {j, 0, n/i}]]];
A[n_, k_] :=
 Sum[Binomial[n - 1, j - 1] n^(n - j) b[j, k], {j, 0, n}];
a[n_] := A[n, 5] - A[n, 6];
a /@ Range[5, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A246049.

Sequence in context: A184274 A093456 A189412 * A246612 A289635 A105187

Adjacent sequences: A246189 A246190 A246191 * A246193 A246194 A246195

Keyword

nonn

Author

Alois P. Heinz, Aug 18 2014

Status

approved