A321254 - OEIS

%I #6 Nov 01 2018 18:22:41

%S 1,3,0,6,0,0,16,1,0,0,37,3,0,0,0,105,18,2,0,0,0,279,68,7,0,0,0,0,817,

%T 293,46,3,0,0,0,0,2387,1141,228,17,1,0,0,0,0,7269,4511,1189,135,9,0,0,

%U 0,0,0

%N Regular triangle where T(n,k) is the number of non-isomorphic connected multiset partitions of weight n with multiset density -1 <= k <= n-2.

%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.

%e Triangle begins:

%e      1

%e      3    0

%e      6    0    0

%e     16    1    0    0

%e     37    3    0    0    0

%e    105   18    2    0    0    0

%e    279   68    7    0    0    0    0

%e    817  293   46    3    0    0    0    0

%e   2387 1141  228   17    1    0    0    0    0

%e   7269 4511 1189  135    9    0    0    0    0    0

%Y First column is A321229. Row sums are A007718.

%Y Cf. A007716, A317672, A321155, A321194, A321253, A321255, A321256.

%K nonn,tabl

%O 1,2

%A _Gus Wiseman_, Nov 01 2018