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A241980 Number of endofunctions on [n] where all cycle lengths are equal. 4
1, 1, 4, 24, 206, 2300, 31742, 522466, 9996478, 218088504, 5344652492, 145386399554, 4347272984936, 141737636485588, 5004538251283846, 190247639729155110, 7747479351505166738, 336492490519027631984, 15526758954835131888980, 758548951300064645742034 (list; graph; refs; listen; history; text; internal format)
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 * A297218 A010039 A245407

Adjacent sequences:  A241977 A241978 A241979 * A241981 A241982 A241983

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 10 2014

STATUS

approved

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Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)