OFFSET
0,3
COMMENTS
Note that here the root is not allowed to be part of the sequence of cycles. We select a root and then form sequences from the cycles in the permutations of the remaining n-1 elements. Cf. A218817. - Geoffrey Critzer, Nov 06 2012
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..150
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 828
FORMULA
E.g.f.: -1/(-1+log(-1/(-1+x)))*x.
a(n) = n*A007840(n-1). a(n) = n!*Sum_{k=0..n-1} a(k)/k!/(n-k) for n>=1 with a(0)=0. - Paul D. Hanna, Jul 19 2006
a(n) ~ n! * exp(n-1) / (exp(1)-1)^n. - Vaclav Kotesovec, Mar 16 2014
MAPLE
spec := [S, {C=Cycle(Z), B=Sequence(C), S=Prod(Z, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
nn=20; a=Log[1/(1-x)]; Range[0, nn]!CoefficientList[Series[x/(1-a) , {x, 0, nn}], x] (* Geoffrey Critzer, Nov 06 2012 *)
PROG
(PARI) a(n)=n!*polcoeff(x/(1+log(1-x +x*O(x^n))), n) \\ Paul D. Hanna, Jul 19 2006
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved