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

Author

Alois P. Heinz, Aug 18 2014

Keywords

• nonn

Links

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

Crossrefs

Column k=6 of A246049.

Programs

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);

Formula

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