%I A133262
%S A133262 1,4,8,172,5204,222716,12509188,889421564,78097622276,8312906703868,
%T A133262 1056520142488580,158263730949406716,27626236450406776836,
%U A133262 5563092167972597137404,1280742543230231763615748,334405228960123174787678204,
               98317121153947856929753989124,32339023133437156084762282819580,11831483864832785151824395066146820,
               4789379698138059405310741712024371196
%N A133262 Number of two-dimensional simple permutations.
%C A133262 A two-dimensional permutation of n is a vector of three permutations, 
               with the first element being the identity permutation. For example, 
               ( (1 2 3) (1 3 2) (3 1 2) ) is a two-dimensional permutation of 3. 
               The example is a simple two-dimensional permutation because none 
               of the intervals of length 2 in the permutations is common among 
               all three. On the other hand, ( (1 2 3) (1 3 2) (2 3 1) ) is not 
               simple because the intervals covering 2 and 3 are common among all 
               three permutations.
%D A133262 M. H. Albert, M. D. Atkinson and M. Klazar. The enumeration of simple 
               permutations. J. Integer Sequences 6 (2003), 03.4.4.
%H A133262 Hao Zhang and Daniel Gildea, <a href="http://www.cs.rochester.edu/~gildea/
               pubs/zhang-gildea-jis07.pdf">Enumeration of Factorizable Multi-Dimensional 
               Permutations</a>, J. Integer Sequences 10 (2007), Article 07.5.8.
%Y A133262 Cf. A006318, A111111.
%Y A133262 Sequence in context: A060239 A127943 A012498 this_sequence A120822 A013065 
               A013096
%Y A133262 Adjacent sequences: A133259 A133260 A133261 this_sequence A133263 A133264 
               A133265
%K A133262 nonn
%O A133262 1,2
%A A133262 Hao Zhang and Daniel Gildea (zhanghao(AT)cs.rochester.edu), Oct 15 2007
%E A133262 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 10 2008