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

%I A290961 #15 Mar 07 2022 07:55:18
%S A290961 1,1,2,6,24,840,720,5040,40320,59814720,3628800,83701537920,479001600,
%T A290961 26980643289600,2642646473026560,1307674368000,20922789888000,
%U A290961 41837259585747225600,6402373705728000,598354114828973074790400,18160977780223038067507200
%N A290961 Number of endofunctions on [n] such that the LCM of their cycle lengths equals n.
%H A290961 Alois P. Heinz, <a href="/A290961/b290961.txt">Table of n, a(n) for n = 1..389</a>
%F A290961 a(n) = A222029(n,n).
%p A290961 b:= proc(n, m) option remember; `if`(n=0, x^m, add((j-1)!*
%p A290961       b(n-j, ilcm(m, j))*binomial(n-1, j-1), j=1..n))
%p A290961     end:
%p A290961 a:= n-> add(coeff(b(j, 1), x, n)*n^(n-j)*binomial(n-1, j-1), j=0..n):
%p A290961 seq(a(n), n=1..25);
%t A290961 b[n_, m_] := b[n, m] = If[n == 0, x^m, Sum[(j - 1)!*
%t A290961      b[n - j, LCM[m, j]]*Binomial[n - 1, j - 1], {j, 1, n}]];
%t A290961 a[n_] := Sum[Coefficient[b[j, 1], x, n]*n^(n-j)*Binomial[n-1, j-1], {j, 0, n}];
%t A290961 Table[a[n], {n, 1, 25}] (* _Jean-François Alcover_, Mar 07 2022, after _Alois P. Heinz_ *)
%Y A290961 Main diagonal of A222029.
%Y A290961 Cf. A074351 (the same for permutations).
%K A290961 nonn
%O A290961 1,3
%A A290961 _Alois P. Heinz_, Aug 15 2017