0,3

This sequence and -A000262 with the first term set to 1 form a reciprocal pair under the list partition transform and associated operations described in A133314. - Tom Copeland (tcjpn(AT)msn.com), Oct 21 2007

T. S. Motzkin, Sorting numbers ...: for a link to this paper see A000262.

T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.

N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.

a(n) = n!*Lag{n,(.)!*Lag[.,P(.,2),0],-1} = P(n,2) - n*P(n-1,2) umbrally, where P(j,t) are the polynomials in A131758 and Lag(n,x,a) are the associated Laguerre polynomials of order a; that is, the sequence is given by an iterated combinatorial Laguerre transform, of mixed order, of a set of polynomials related to the polylogarithms, which reduces to a simple finite difference. - Tom Copeland (tcjpn(AT)msn.com), Sep 30 2007=20

E.g.f.: 1/(2-exp(x/(1-x))). Lah transform of preferential arrangements: Sum_{k=0..n} n!/k!*binomial(n-1, k-1)*A000670(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 28 2003

with(combstruct); SeqSetSeqL := [T, {T=Sequence(S), S=Set(U, card >= 1), U=Sequence(Z, card >=1)}, labeled]; [seq(count(%, size=j), j=1..12)];

Sequence in context: A004208 A112698 A025168 this_sequence A050351 A129137 A055869

Adjacent sequences: A084355 A084356 A084357 this_sequence A084359 A084360 A084361

nonn

N. J. A. Sloane (njas(AT)research.att.com), Jun 22 2003