%I A072447
%S A072447 1,1,8,378,252000,17197930224
%N A072447 Number of subsets S of the power set P{1,2,...,n} such that: {1}, {2},
               ..., {n} are all elements of S; {1,2,...n} is an element of S; if 
               X and Y are elements of S and X and Y have a non-empty intersection, 
               then the union of X and Y is an element of S.
%H A072447 Wim van Dam, <a href="http://www.cs.berkeley.edu/~vandam/subpowersets/
               sequences.html">Sub Power Set Sequences</a>
%e A072447 a(3)=8 because of the 8 sets: {{1}, {2}, {3}, {1, 2, 3}}; {{1}, {2}, 
               {3}, {1, 2}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 3}, {1, 2, 3}}; {{1}, 
               {2}, {3}, {2, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {1, 
               2, 3}}; {{1}, {2}, {3}, {1, 2}, {2, 3}, {1, 2, 3}}; {{1}, {2}, {3}, 
               {1, 3}, {2, 3}, {1, 2, 3}}; {{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, 
               {1, 2, 3}}.
%Y A072447 Cf. A072444, A072445, A072446.
%Y A072447 Sequence in context: A015507 A167256 A038016 this_sequence A151932 A096205 
               A162445
%Y A072447 Adjacent sequences: A072444 A072445 A072446 this_sequence A072448 A072449 
               A072450
%K A072447 nonn
%O A072447 1,3
%A A072447 Wim van Dam (vandam(AT)cs.berkeley.edu), Jun 18 2002