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A290961 Number of endofunctions on [n] such that the LCM of their cycle lengths equals n. 3

%I

%S 1,1,2,6,24,840,720,5040,40320,59814720,3628800,83701537920,479001600,

%T 26980643289600,2642646473026560,1307674368000,20922789888000,

%U 41837259585747225600,6402373705728000,598354114828973074790400,18160977780223038067507200

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

%H Alois P. Heinz, <a href="/A290961/b290961.txt">Table of n, a(n) for n = 1..389</a>

%F a(n) = A222029(n,n).

%p b:= proc(n, m) option remember; `if`(n=0, x^m, add((j-1)!*

%p b(n-j, ilcm(m, j))*binomial(n-1, j-1), j=1..n))

%p end:

%p a:= n-> add(coeff(b(j, 1), x, n)*n^(n-j)*binomial(n-1, j-1), j=0..n):

%p seq(a(n), n=1..25);

%Y Main diagonal of A222029.

%Y Cf. A074351 (the same for permutations).

%K nonn

%O 1,3

%A _Alois P. Heinz_, Aug 15 2017

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Last modified October 16 20:35 EDT 2019. Contains 328103 sequences. (Running on oeis4.)