A246193 Number of endofunctions on [n] where the smallest cycle length equals 6.

120, 5040, 161280, 4898880, 151200000, 4870182240, 165549605760, 5964805154880, 228051369786240, 9247246914906000, 397146441431900160, 18033691478872567680, 864117601222345666560, 43606402916521420059840, 2312912761606956925440000, 128696545326829348772023680

Offset

6,1

Links

Alois P. Heinz, Table of n, a(n) for n = 6..200

Formula

a(n) ~ (exp(-137/60) - exp(-49/20)) * n^n. - Vaclav Kotesovec, Aug 21 2014

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
      add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*
      b(n-i*j, i+1), j=0..n/i)))
    end:
A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):
a:= n-> A(n, 6) -A(n, 7):
seq(a(n), n=6..25);

Crossrefs

Column k=6 of A246049.

Sequence in context: A174686 A140907 A072419 * A246613 A031145 A126245

Adjacent sequences: A246190 A246191 A246192 * A246194 A246195 A246196

Keyword

nonn

Author

Alois P. Heinz, Aug 18 2014

Status

approved