A052522 - OEIS

%I #19 Jul 04 2018 05:44:02

%S 0,1,0,2,6,64,540,6908,93744,1542616,28057800,576840032,13029824016,

%T 323152349584,8698499671680,252998272144928,7900336700736864,

%U 263731233726459136,9370598887948893120,353114271843930110912

%N Number of labeled mobiles with cycles of length at least 3.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=90">Encyclopedia of Combinatorial Structures 90</a>

%F E.g.f.: (exp(RootOf(2*_Z*exp(_Z)^2 - 5*exp(_Z)^2 + 6*exp(_Z) + 2*x*exp(_Z)^2-1)) -1) / exp(RootOf(2*_Z*exp(_Z)^2 - 5*exp(_Z)^2 + 6*exp(_Z) + 2*x*exp(_Z)^2-1)).

%F E.g.f. A(x) is the series is reversion of 2*x-1/2*x^2-log(1+x). a(n) = (sum(k=0..n-1, (n+k-1)! * sum(j=0..k, 1/(k-j)! * sum(l=0..j, 1/l! * sum(i=0..l, ((-1)^(i+n+l-1) * 2^(l-2*i) * binomial(l,i) * stirling1(n+j-i-l-1,j-l))/(n+j-i-l-1)!))))), n > 0. - _Vladimir Kruchinin_, Feb 18 2012

%p spec := [S,{S=Union(B,Z),B=Cycle(S,3 <= card)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%o (Maxima) a(n):=(sum((n+k-1)! * sum(1/(k-j)! * sum(1/l! * sum(((-1)^(i+n+l-1) * 2^(l-2*i) * binomial(l,i) * stirling1(n+j-i-l-1,j-l)) / (n+j-i-l-1)!, i,0,l), l,0,j), j,0,k), k,0,n-1)); /* _Vladimir Kruchinin_, Feb 18 2012 */

%K easy,nonn

%O 0,4

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000