A052896 E.g.f.: (exp(exp(x)-1)-1)^2.

0, 0, 2, 12, 64, 350, 2024, 12460, 81638, 567888, 4180848, 32470834, 265219332, 2271692124, 20350705418, 190216812260, 1850993707960, 18714559108142, 196237054861920, 2130518566431620, 23912733627261670, 277078872201375976, 3310142647325149512

Offset: 0

Author

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

Keywords

• easy
• nonn

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

Crossrefs

Equals twice A000558.

Cf. A001861, A008277.

Programs

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]

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).

Extensions

New name using e.g.f., Vaclav Kotesovec, Nov 20 2017