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A291116 Number of endofunctions on [n] such that the LCM of their cycle lengths equals ten. 2
0, 0, 0, 0, 0, 0, 0, 504, 32256, 1460592, 59814720, 2403157680, 98055619200, 4129943329512, 180976836968928, 8281570545448200, 396324506640142080, 19840151844921504096, 1038497761573246945152, 56790713866712335971552, 3241264004352759793685760 (list; graph; refs; listen; history; text; internal format)
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 xrange(1, n + 1)])

def a(n): return sum([b(j, 1)*n**(n - j)*binomial(n - 1, j - 1) for j in xrange(n + 1)])

print map(a, xrange(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

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Last modified February 22 20:30 EST 2019. Contains 320404 sequences. (Running on oeis4.)