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A291115 Number of endofunctions on [n] such that the LCM of their cycle lengths equals nine. 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 40320, 4032000, 266112000, 15008716800, 794060467200, 41179634496000, 2142915046272000, 113401428940800000, 6150985123214131200, 343578020565722342400, 19818131438503157760000, 1182304993642509574656000, 73005714001076187082752000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

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

FORMULA

a(n) ~ (3*exp(13/9) - 2*exp(4/3)) * 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))))(9)

    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>9, 0, If[n==0, If[m==9, 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>9 else (1 if m==9 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=9 of A222029.

Sequence in context: A179063 A246196 A246616 * A246219 A045516 A160318

Adjacent sequences:  A291112 A291113 A291114 * A291116 A291117 A291118

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 17 2017

STATUS

approved

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Last modified February 23 18:13 EST 2019. Contains 320437 sequences. (Running on oeis4.)