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A241980 Number of endofunctions on [n] where all cycle lengths are equal.

%I A241980 #18 Aug 18 2014 21:38:41
%S A241980 1,1,4,24,206,2300,31742,522466,9996478,218088504,5344652492,
%T A241980 145386399554,4347272984936,141737636485588,5004538251283846,
%U A241980 190247639729155110,7747479351505166738,336492490519027631984,15526758954835131888980,758548951300064645742034
%N A241980 Number of endofunctions on [n] where all cycle lengths are equal.
%H A241980 Alois P. Heinz, <a href="/A241980/b241980.txt">Table of n, a(n) for n = 0..300</a>
%F A241980 a(n) = Sum_{j=0..n} C(n-1,j-1) * n^(n-j) * A005225(j).
%F A241980 a(n) = Sum_{k=0..n} A243098(n,k).
%p A241980 with(numtheory):
%p A241980 b:= n-> `if`(n=0, 1, n!*add((d!*(n/d)^d)^(-1), d=divisors(n))):
%p A241980 a:= n-> add(binomial(n-1, j-1)*n^(n-j)*b(j), j=0..n):
%p A241980 seq(a(n), n=0..25);
%t A241980 nn=20;t[x_]:=Sum[n^(n-1)x^n/n!,{n,1,nn}];Range[0,nn]!CoefficientList[Series[1+Sum[Exp[t[x]^i/i]-1,{i,1,nn}],{x,0,nn}],x] (* _Geoffrey Critzer_, Aug 11 2014 *)
%Y A241980 Cf. A005225, A061356, A212789, A242027 (column k=1).
%Y A241980 Row sums of A243098.
%K A241980 nonn
%O A241980 0,3
%A A241980 _Alois P. Heinz_, Aug 10 2014