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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 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=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 May 17 19:51 EDT 2022. Contains 353778 sequences. (Running on oeis4.)