A246610 Number of endofunctions on [n] whose cycle lengths are multiples of 3.

1, 0, 0, 2, 24, 300, 4480, 78750, 1591296, 36355256, 927244800, 26127386010, 806251494400, 27046291980708, 980094896062464, 38158333538165750, 1588601646620835840, 70427042234715548400, 3312574102411273437184, 164767312911755127462066, 8641342923227371929600000

Offset

0,4

Links

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

Formula

E.g.f.: 1/(1+LambertW(-x)^3)^(1/3). - Vaclav Kotesovec, Sep 01 2014

a(n) ~ GAMMA(5/6) * n^(n-1/3) / (12^(1/3) * sqrt(Pi)) * (1 - 2^(7/6) * GAMMA(1/3)^3 / (9 * Pi^(3/2) * sqrt(n))). - 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+3)*(i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
    end:
a:= a->add(b(j, 3)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..20);

Mathematica

CoefficientList[Series[1/(1+LambertW[-x]^3)^(1/3), {x, 0, 20}], x] * Range[0, 20]!  (* Vaclav Kotesovec, Sep 01 2014 *)

Crossrefs

Column k=3 of A246609.

Sequence in context: A336310 A065513 A246190 * A119491 A001864 A099045

Adjacent sequences: A246607 A246608 A246609 * A246611 A246612 A246613

Keyword

nonn

Author

Alois P. Heinz, Aug 31 2014

Status

approved