A052522 Number of labeled mobiles with cycles of length at least 3.

0, 1, 0, 2, 6, 64, 540, 6908, 93744, 1542616, 28057800, 576840032, 13029824016, 323152349584, 8698499671680, 252998272144928, 7900336700736864, 263731233726459136, 9370598887948893120, 353114271843930110912

Offset

0,4

Links

Table of n, a(n) for n=0..19.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 90

Formula

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)).

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

Maple

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

Prog

(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 */

Crossrefs

Sequence in context: A139695 A347949 A241590 * A193609 A061999 A066756

Adjacent sequences: A052519 A052520 A052521 * A052523 A052524 A052525

Keyword

easy,nonn

Author

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

Status

approved