%I A092920
%S A092920 1,1,2,4,9,22,58,164,496,1601,5502,20075,77531,315947,1354279,6087421,
%T A092920 28611385,140239297,715116827,3785445032,20760746393,117759236340,
%U A092920 689745339984,4165874930885,25911148634728,165775085602106
%N A092920 Number of strongly monotone partitions of n.
%C A092920 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.
%C A092920 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
%C A092920 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
%H A092920 A. Claesson and T. Mansour, <a href="http://www.arXiv.org/abs/math.CO/
               0107044">Permutations avoiding a pair of generalized patterns...</
               a>.
%F A092920 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.
%p A092920 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)
%Y A092920 Sequence in context: A059019 A121953 A024427 this_sequence A035053 A000571 
               A077003
%Y A092920 Adjacent sequences: A092917 A092918 A092919 this_sequence A092921 A092922 
               A092923
%K A092920 nonn
%O A092920 0,3
%A A092920 Ralf Stephan, Apr 17 2004
%E A092920 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 13 2005