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

0,4

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

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

Sequence in context: A147063 A357640 A007865 * A213331 A218153 A319642

Adjacent sequences: A052809 A052810 A052811 * A052813 A052814 A052815

Keyword

easy,nonn

Author

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

Extensions

More terms from Vladeta Jovovic, Sep 17 2002

Status

approved