A241980 Number of endofunctions on [n] where all cycle lengths are equal.

1, 1, 4, 24, 206, 2300, 31742, 522466, 9996478, 218088504, 5344652492, 145386399554, 4347272984936, 141737636485588, 5004538251283846, 190247639729155110, 7747479351505166738, 336492490519027631984, 15526758954835131888980, 758548951300064645742034

Offset: 0

Author

Alois P. Heinz, Aug 10 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A005225, A061356, A212789, A242027 (column k=1).

Row sums of A243098.

Programs

Maple

with(numtheory):
b:= n-> `if`(n=0, 1, n!*add((d!*(n/d)^d)^(-1), d=divisors(n))):
a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j), j=0..n):
seq(a(n), n=0..25);

Mathematica

nn=20;t[x_]:=Sum[n^(n-1)x^n/n!,{n,1,nn}];Range[0,nn]!CoefficientList[Series[1+Sum[Exp[t[x]^i/i]-1,{i,1,nn}],{x,0,nn}],x] (* Geoffrey Critzer, Aug 11 2014 *)

Formula

a(n) = Sum_{j=0..n} C(n-1,j-1) * n^(n-j) * A005225(j).

a(n) = Sum_{k=0..n} A243098(n,k).