OFFSET
0,4
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
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
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from Vladeta Jovovic, Sep 17 2002
STATUS
approved