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A291110 Number of endofunctions on [n] such that the LCM of their cycle lengths equals four. 2
0, 0, 0, 0, 6, 150, 3240, 71610, 1692180, 43296120, 1202014800, 36144686160, 1173334341960, 40964232699390, 1532291272031520, 61185138170697450, 2599160146594218480, 117091760635760465520, 5577733223175044859840, 280195572152151651031200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

a(n) ~ (3*exp(7/4) - 2*exp(3/2)) * 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))))(4)

    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

b[n_, m_] := b[n, m] = With[{k = 4}, If[m > k, 0, If[n == 0, If[m == k, 1, 0], Sum[b[n - j, LCM[m, j]] Binomial[n-1, j - 1] (j-1)!, {j, 1, n}]]]];

a[n_] := If[n == 0, 0, Sum[b[j, 1] n^(n-j) Binomial[n-1, j-1], {j, 0, n}]];

a /@ Range[0, 22] (* Jean-Fran├žois Alcover, Dec 29 2020, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A222029.

Sequence in context: A056418 A346694 A070025 * A246214 A065946 A222051

Adjacent sequences:  A291107 A291108 A291109 * A291111 A291112 A291113

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 17 2017

STATUS

approved

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Last modified May 17 17:52 EDT 2022. Contains 353778 sequences. (Running on oeis4.)