A246951 Number of endofunctions f on [n] such that the number of cycles of f is a multiple of 3 for each size that is a multiple of 3.

1, 1, 4, 25, 224, 2625, 37936, 651553, 12963840, 293219361, 7429984000, 208486630121, 6417388432896, 214990745268065, 7787303908091904, 303250854519320625, 12633932936000045056, 560712315504995304897, 26410168773292930375680, 1315770870814835066545081

Offset: 0

Author

Alois P. Heinz, Sep 08 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..380

Crossrefs

Cf. A212599.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(`if`(irem(j, igcd(i, 3))<>0, 0, b(n-i*j, i-1)*
      (i-1)!^j*multinomial(n, n-i*j, i$j)/j!), j=0..n/i)))
    end:
a:= n-> add(b(j$2)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25);