OFFSET
0,3
COMMENTS
Previous name was: A simple grammar.
a(n) is the number of ways to place n labeled balls into unlabeled (but two-colored) boxes so that at least one box is red and one box is blue. - Geoffrey Critzer, Oct 16 2011
LINKS
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 872
FORMULA
E.g.f.: exp(exp(x)-1)^2 - 2*exp(exp(x)-1) + 1.
For n >= 1: a(n) = Sum_{k=0...n} Stirling2(n,k)*(2^k-2) where Stirling2(n,k) is the number of set partitions of {1,2,...,n} into exactly k blocks (A008277).
MAPLE
spec := [S, {B=Set(Z, 1 <= card), C=Set(B, 1 <= card), S=Prod(C, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
a=Exp[Exp[x]-1]; Range[0, 20]! CoefficientList[Series[(a-1)^2, {x, 0, 20}], x]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
New name using e.g.f., Vaclav Kotesovec, Nov 20 2017
STATUS
approved