A246617 Number of endofunctions on [n] whose cycle lengths are multiples of 10.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 362880, 39916800, 2874009600, 175394419200, 9967384627200, 551675124000000, 30471021291110400, 1703458301210265600, 97213825272736972800, 5693251850259515942400, 343266731083210449715200, 21349233350716392722764800

Offset

0,11

Comments

In general, column k of A246609 is (for k > 1) asymptotic to n^(n-1/2 + 1/(2*k)) * sqrt(2*Pi) / (2^(1/(2*k)) * k^(1/k) * Gamma(1/(2*k))) * (1 - (3*k-1)*(k-1) * sqrt(2/n) * Gamma(1/(2*k)) / (12 * k^2 * Gamma(1/2 + 1/(2*k)))). - Vaclav Kotesovec, Sep 01 2014

Links

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

Formula

E.g.f.: 1/(1-LambertW(-x)^10)^(1/10). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ n^(n-9/20) * 2^(7/20) * sqrt(Pi) / (5^(1/10) * Gamma(1/20)) * (1 - 87 * sqrt(2/n) * Gamma(1/20) / (400 * Gamma(11/20))). - Vaclav Kotesovec, Sep 01 2014

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(i>n, 0, add(b(n-i*j, i+10)*(i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
    end:
a:= a->add(b(j, 10)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);

Mathematica

CoefficientList[Series[1/(1-LambertW[-x]^10)^(1/10), {x, 0, 20}], x] * Range[0, 20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

Crossrefs

Column k=10 of A246609.

Sequence in context: A213871 A179064 A246197 * A246220 A160319 A227671

Adjacent sequences: A246614 A246615 A246616 * A246618 A246619 A246620

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2014

Status

approved