|
%I #8 Nov 01 2018 18:22:48
%S 0,0,2,3,8,19,60,183,643,2355,9393
%N Number of connected multiset partitions with multiset density -1, of strongly normal multisets of size n, with no singletons.
%C The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.
%C A multiset is normal if it spans an initial interval of positive integers, and strongly normal if in addition its multiplicities are weakly decreasing.
%e The a(2) = 2 through a(5) = 19 multiset partitions:
%e {{1,1}} {{1,1,1}} {{1,1,1,1}} {{1,1,1,1,1}}
%e {{1,2}} {{1,1,2}} {{1,1,1,2}} {{1,1,1,1,2}}
%e {{1,2,3}} {{1,1,2,2}} {{1,1,1,2,2}}
%e {{1,1,2,3}} {{1,1,1,2,3}}
%e {{1,2,3,4}} {{1,1,2,2,3}}
%e {{1,1},{1,1}} {{1,1,2,3,4}}
%e {{1,1},{1,2}} {{1,2,3,4,5}}
%e {{1,2},{1,3}} {{1,1},{1,1,1}}
%e {{1,1},{1,1,2}}
%e {{1,1},{1,2,2}}
%e {{1,1},{1,2,3}}
%e {{1,2},{1,1,1}}
%e {{1,2},{1,1,3}}
%e {{1,2},{1,3,4}}
%e {{1,3},{1,1,2}}
%e {{1,3},{1,2,2}}
%e {{1,3},{1,2,4}}
%e {{1,4},{1,2,3}}
%e {{2,3},{1,1,2}}
%Y Cf. A000272, A030019, A052888, A134954, A304867, A317672, A321228, A321229, A321253.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Nov 01 2018
|
