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

0,3

Links

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

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).

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 *)

Crossrefs

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

Row sums of A243098.

Sequence in context: A240429 A240297 A050388 * A368267 A297218 A010039

Adjacent sequences: A241977 A241978 A241979 * A241981 A241982 A241983

Keyword

nonn

Author

Alois P. Heinz, Aug 10 2014

Status

approved