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

0,3

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

Table of n, a(n) for n=0..22.

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

Equals twice A000558.

Cf. A001861, A008277.

Sequence in context: A006646 A087635 A180038 * A215128 A190155 A025599

Adjacent sequences: A052893 A052894 A052895 * A052897 A052898 A052899

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