A052812 A simple grammar: power set of pairs of sequences.

1, 0, 1, 2, 3, 6, 9, 16, 24, 42, 63, 102, 157, 244, 373, 570, 858, 1290, 1930, 2858, 4228, 6208, 9084, 13216, 19175, 27666, 39804, 57020, 81412, 115820, 164264, 232178, 327220, 459796, 644232, 900214, 1254554, 1743896, 2418071, 3344896, 4616026

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Number of partitions of n objects of two colors into distinct parts, where each part must contain at least one of each color. - Franklin T. Adams-Watters, Dec 28 2006

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 776

Crossrefs

Cf. A026007, A052847, A219555, A255834, A255835.

Programs

Maple

spec := [S,{B=Sequence(Z,1 <= card),C=Prod(B,B),S= PowerSet(C)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

nmax=50; CoefficientList[Series[Product[(1+x^k)^(k-1),{k,1,nmax}],{x,0,nmax}],x] (* Vaclav Kotesovec, Mar 07 2015 *)

Formula

G.f.: exp(Sum((-1)^(j[1]+1)*(x^j[1])^2/(x^j[1]-1)^2/j[1], j[1]=1 .. infinity))

G.f.: Product_{k>=1} (1+x^k)^(k-1). - Vladeta Jovovic, Sep 17 2002

Weigh transform of b(n) = n-1. - Franklin T. Adams-Watters, Dec 28 2006

a(n) ~ Zeta(3)^(1/6) * exp(-Pi^4/(1296*Zeta(3)) - Pi^2 * n^(1/3) / (3^(4/3) * 2^(5/3) * Zeta(3)^(1/3)) + (3/2)^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (2^(1/4) * 3^(1/3) * n^(2/3) * sqrt(Pi)), where Zeta(3) = A002117. - Vaclav Kotesovec, Mar 07 2015

Extensions

More terms from Vladeta Jovovic, Sep 17 2002