# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a052812
Showing 1-1 of 1

%I A052812 #18 Apr 18 2017 07:04:08
%S A052812 1,0,1,2,3,6,9,16,24,42,63,102,157,244,373,570,858,1290,1930,2858,
%T A052812 4228,6208,9084,13216,19175,27666,39804,57020,81412,115820,164264,
%U A052812 232178,327220,459796,644232,900214,1254554,1743896,2418071,3344896,4616026
%N A052812 A simple grammar: power set of pairs of sequences.
%C A052812 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 A052812 Vaclav Kotesovec, <a href="/A052812/b052812.txt">Table of n, a(n) for n = 0..1000</a>
%H A052812 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=776">Encyclopedia of Combinatorial Structures 776</a>
%F A052812 G.f.: exp(Sum((-1)^(j[1]+1)*(x^j[1])^2/(x^j[1]-1)^2/j[1], j[1]=1 .. infinity))
%F A052812 G.f.: Product_{k>=1} (1+x^k)^(k-1). - _Vladeta Jovovic_, Sep 17 2002
%F A052812 Weigh transform of b(n) = n-1. - _Franklin T. Adams-Watters_, Dec 28 2006
%F A052812 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 A052812 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 A052812 nmax=50; CoefficientList[Series[Product[(1+x^k)^(k-1),{k,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Mar 07 2015 *)
%Y A052812 Cf. A026007, A052847, A219555, A255834, A255835.
%K A052812 easy,nonn
%O A052812 0,4
%A A052812 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052812 More terms from _Vladeta Jovovic_, Sep 17 2002

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE