login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A246529 Number of endofunctions on [n] whose cycle lengths are divisors of 9. 2
1, 1, 3, 18, 157, 1776, 24687, 407464, 7792857, 169594560, 4141165051, 112178655744, 3339749183157, 108422228887168, 3812520677598375, 144372964560581376, 5858088633723823153, 253575577033176047616, 11664031615012086920307, 568166632439929892761600 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 21:30 EDT 2021. Contains 344003 sequences. (Running on oeis4.)