0,3

A partition is strongly monotone if its blocks can be written in increasing order of their least element and increasing order of their greatest element, simultaneously.

a(n) = number of nonnesting partitions of [n]. A nonnesting partition is one in which no block is contained in the span of another, where span denotes the interval from smallest to largest entries. In fact, the strongly monotone partitions of [n] coincide with the nonnesting partitions of [n]. - David Callan (callan(AT)stat.wisc.edu), Sep 20 2007

a(n) = number of strongly nonoverlapping partitions of [n] where "strongly nonoverlapping" means nonoverlapping (see A006789 for definition) and, in addition, no singleton block is a subset of the span (interval from minimum to maximum) of another block. For example, 13-24 is nonnesting and 14-23 is strongly nonoverlapping but neither has the other property. The Motzkin number M_n (A001006) counts strongly noncrossing partitions of [n]. - David Callan (callan(AT)stat.wisc.edu), Sep 20 2007

A. Claesson and T. Mansour, Permutations avoiding a pair of generalized patterns....

G.f.: sum(n>=0, a(n)x^n) = 1/(1-x-x^2/(1-x-x^2/(1-2x-x^2/(1-3x-x^2/...))) = 1/(1-x-x^2*B(x)) where B(x) is g.f. for the Bessel numbers A006789.

G:=1/(1-x-x^2/(1-x-x^2/(1-2*x-x^2/(1-3*x-x^2/(1-4*x-x^2/(1-5*x-x^2/(1-6*x-x^2/(1-7*x-x^2/(1-8*x-x^2/(1-9*x-x^2/(1-10*x-x^2/(1-11*x-x^2/(1-12*x-x^2/(1-13*x-x^2/(1-14*x-x^2/(1-15*x-x^2/(1-16*x-x^2/(1-17*x-x^2)))))))))))))))))):Gser:=series(G, x=0, 32): 1, seq(coeff(Gser, x^n), n=1..28); (Deutsch)

Sequence in context: A059019 A121953 A024427 this_sequence A035053 A000571 A077003

Adjacent sequences: A092917 A092918 A092919 this_sequence A092921 A092922 A092923

nonn

Ralf Stephan, Apr 17 2004

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 13 2005