0,3

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Index entries for sequences related to posets

Related to A000798 by A000798(n) = Sum Stirling2(n, k)*A001035(k).

Related to A000112 by Erne's formulae: A001035(n+1)=-s(n, 1), A001035(n+2)=n*A001035(n+1)+s(n, 2), A001035(n+3)=binomial(n+4, 2)*A001035(n+2)-s(n, 3), where s(n, k)=sum(binomial(n+k-1-m, k-1)*binomial(n+k, m)*sum((m!)/(number of automorphisms of P)*(-(number of antichains of P))^k, P an unlabeled poset with m elements), m=0..n).

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 1, Chap. 3, page 98, Fig. 3-1 shows the unlabeled posets with <= 4 points.

Cf. A000798 (labeled topologies), A001930 (unlabeled topologies), A000112 (unlabeled posets), A006057.

Sequence in context: A005647 A158876 A001833 * A166380 A136652 A136504

Adjacent sequences:  A001032 A001033 A001034 * A001036 A001037 A001038

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).

Terms for n=15 and 16 from Jobst Heitzig (heitzig(AT)math.uni-hannover.de), Jul 03 2000

a(17) and a(18) from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008