A246529 Number of endofunctions on [n] whose cycle lengths are divisors of 9.

1, 1, 3, 18, 157, 1776, 24687, 407464, 7792857, 169594560, 4141165051, 112178655744, 3339749183157, 108422228887168, 3812520677598375, 144372964560581376, 5858088633723823153, 253575577033176047616, 11664031615012086920307, 568166632439929892761600

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..350

Formula

E.g.f.: exp(Sum_{d|9} (-LambertW(-x))^d/d).

a(n) - A246523(n) is a multiple of 40320. - M. F. Hasler, Oct 26 2014

Maple

with(numtheory):
egf:= k-> exp(add((-LambertW(-x))^d/d, d=divisors(k))):
a:= n-> n!*coeff(series(egf(9), x, n+1), x, n):
seq(a(n), n=0..25);
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)*
      (i-1)!^j, j=0..`if`(irem(9, i)=0, n/i, 0))))
    end:
a:= n-> add(b(j, min(9, j))*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Crossrefs

Column k=9 of A246522.

Sequence in context: A181374 A060913 A246523 * A305824 A116956 A166887

Adjacent sequences: A246526 A246527 A246528 * A246530 A246531 A246532

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2014

Status

approved