%I #6 Mar 31 2012 13:23:38
%S 1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,2,1,1,1,1,1,1,1,1,2,3,3,2,1,1,1,1,
%T 1,1,1,1,1,2,3,3,3,2,1,1,2,3,4,3,2,1,1,3,6,7,6,3,1,1,1,1,1,1,1,1,1,1,
%U 2,3,3,3,3,2,1,1,2,3,4,4,3,2,1,1,3,6,8,8,6,3,1
%N A sequence of rectangular tables with row sums A122401 related to A002865 and A122172.
%C Sequence A002865 gives the number of rows in each rectangular table. A122402 is a subsequence of A122172.
%e There are four cyclic partitions of 6: 6, 42, 33 and 222; therefore the corresponding table is
%e 1 1 1 1 1 1 1
%e 1 2 3 3 3 2 1
%e 1 2 3 4 3 2 1
%e 1 3 6 7 6 3 1
%e The tables begin:
%e 1
%e 0
%e 1 1 1
%e 1 1 1 1
%e 1 1 1 1 1
%e 1 2 3 2 1
%e 1 1 1 1 1 1
%e 1 2 3 3 2 1
%e ...
%Y Cf. A002865 A122172 A122401.
%K easy,nonn,tabf
%O 0,16
%A _Alford Arnold_, Sep 02 2006