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

0,3

Links

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

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);

Crossrefs

Cf. A212599.

Sequence in context: A050386 A246524 A246528 * A302587 A302608 A340337

Adjacent sequences: A246948 A246949 A246950 * A246952 A246953 A246954

Keyword

nonn

Author

Alois P. Heinz, Sep 08 2014

Status

approved