%I #18 Apr 18 2017 07:04:08

%S 1,0,1,2,3,6,9,16,24,42,63,102,157,244,373,570,858,1290,1930,2858,

%T 4228,6208,9084,13216,19175,27666,39804,57020,81412,115820,164264,

%U 232178,327220,459796,644232,900214,1254554,1743896,2418071,3344896,4616026

%N A simple grammar: power set of pairs of sequences.

%C 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

%H Vaclav Kotesovec, <a href="/A052812/b052812.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=776">Encyclopedia of Combinatorial Structures 776</a>

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

%F G.f.: Product_{k>=1} (1+x^k)^(k-1). - _Vladeta Jovovic_, Sep 17 2002

%F Weigh transform of b(n) = n-1. - _Franklin T. Adams-Watters_, Dec 28 2006

%F 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

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

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

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

%K easy,nonn

%O 0,4

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

%E More terms from _Vladeta Jovovic_, Sep 17 2002