OFFSET
0,3
COMMENTS
a(n) is the number of forests of rooted unlabeled identity trees. Euler transform of A004111. - Geoffrey Critzer, Oct 13 2012
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 64, Eq. (3.3.15); p. 80, Problem 3.10.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 811
FORMULA
O.g.f.: prod(n>=1, 1/(1 - x^n)^A004111(n) ). - Geoffrey Critzer, Oct 13 2012
MAPLE
spec := [S, {C=Prod(Z, B), B=PowerSet(C), S=Set(C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
# second Maple program:
with(numtheory):
b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(d*
b(d)*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*b(d),
d=divisors(j)) *a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..40); # Alois P. Heinz, Mar 06 2015
MATHEMATICA
nn=35; s[n_, k_]:=s[n, k]=a[n+1-k]+If[n<2k, 0, -s[n-k, k]]; a[1]=1; a[n_]:=a[n]=Sum[a[i]s[n-1, i]i, {i, 1, n-1}]/(n-1); it=Table[a[i], {i, 1, nn}]; CoefficientList[Series[Product[1/(1-x^i)^it[[i]], {i, 1, nn}], {x, 0, nn}], x] (* after code given by Robert A. Russell in A004111 *)
(* Geoffrey Critzer, Oct 13 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
Added more terms, Geoffrey Critzer, Oct 13 2012
STATUS
approved