A291116 Number of endofunctions on [n] such that the LCM of their cycle lengths equals ten.

0, 0, 0, 0, 0, 0, 0, 504, 32256, 1460592, 59814720, 2403157680, 98055619200, 4129943329512, 180976836968928, 8281570545448200, 396324506640142080, 19840151844921504096, 1038497761573246945152, 56790713866712335971552, 3241264004352759793685760

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..387

Formula

a(n) ~ (exp(1) - 2*exp(3/2) - 2*exp(6/5) + 4*exp(9/5)) * n^(n-1). - Vaclav Kotesovec, Aug 18 2017

Maple

b:= proc(n, m) option remember; (k-> `if`(m>k, 0,
      `if`(n=0, `if`(m=k, 1, 0), add(b(n-j, ilcm(m, j))
       *binomial(n-1, j-1)*(j-1)!, j=1..n))))(10)
    end:
a:= n-> add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..22);

Mathematica

Unprotect[Power]; Power[0|0., 0|0.]=1; Protect[Power]; b[n_, m_]:=b[n, m]=If[m>10, 0, If[n==0, If[m==10, 1, 0], Sum[b[n - j, LCM[m, j]] Binomial[n - 1, j - 1](j - 1)!, {j, n}]]]; Table[Sum[b[j, 1]*n^(n -j) Binomial[n - 1, j - 1], {j, 0, n}], {n, 0, 25}] (* Indranil Ghosh, Aug 18 2017 *)

Prog

(Python)
from sympy.core.cache import cacheit
from sympy import binomial, lcm, factorial as f
@cacheit
def b(n, m): return 0 if m>10 else (1 if m==10 else 0) if n==0 else sum([b(n - j, lcm(m, j))*binomial(n - 1, j - 1)*f(j - 1) for j in range(1, n + 1)])
def a(n): return sum([b(j, 1)*n**(n - j)*binomial(n - 1, j - 1) for j in range(n + 1)])
print([a(n) for n in range(26)]) # Indranil Ghosh, Aug 18 2017

Crossrefs

Column k=10 of A222029.

Sequence in context: A013973 A218132 A012744 * A145095 A035293 A278626

Adjacent sequences: A291113 A291114 A291115 * A291117 A291118 A291119

Keyword

nonn

Author

Alois P. Heinz, Aug 17 2017

Status

approved