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%I #9 Oct 29 2018 09:56:08
%S 1,2,1,3,2,1,6,6,4,1,10,14,11,4,1,22,38,38,20,6,1,42,94,111,72,28,6,1,
%T 94,250,348,278,138,42,8,1,203,648,1044,992,596,226,56,8,1,470,1728,
%U 3192,3538,2536,1192,370,76,10,1
%N Regular triangle where T(n,k) is the number of non-isomorphic connected multiset partitions of weight n with density -1 <= k < n-2.
%C The density of a multiset partition of weight n with e parts and v vertices is n - e - v. The weight of a multiset partition is the sum of sizes of its parts.
%e Triangle begins:
%e 1
%e 2 1
%e 3 2 1
%e 6 6 4 1
%e 10 14 11 4 1
%e 22 38 38 20 6 1
%e 42 94 111 72 28 6 1
%e 94 250 348 278 138 42 8 1
%e 203 648 1044 992 596 226 56 8 1
%e 470 1728 3192 3538 2536 1192 370 76 10 1
%e Non-isomorphic representatives of the connected multiset partitions counted in row 5:
%e {1,2,3,4,5} {1,2,3,4,4} {1,2,2,3,3} {1,1,2,2,2} {1,1,1,1,1}
%e {1,4},{2,3,4} {1,2},{2,3,3} {1,2,3,3,3} {1,2,2,2,2}
%e {4},{1,2,3,4} {1,3},{2,3,3} {1,1},{1,2,2} {1},{1,1,1,1}
%e {2},{1,3},{2,3} {2},{1,2,3,3} {1},{1,2,2,2} {1,1},{1,1,1}
%e {2},{3},{1,2,3} {2,3},{1,2,3} {1,2},{1,2,2}
%e {3},{1,3},{2,3} {3},{1,2,3,3} {1,2},{2,2,2}
%e {3},{3},{1,2,3} {3,3},{1,2,3} {2},{1,1,2,2}
%e {1},{2},{2},{1,2} {1},{1},{1,2,2} {2},{1,2,2,2}
%e {2},{2},{2},{1,2} {1},{1,2},{2,2} {2,2},{1,2,2}
%e {1},{1},{1},{1},{1} {1},{2},{1,2,2} {1},{1},{1,1,1}
%e {2},{1,2},{1,2} {1},{1,1},{1,1}
%e {2},{1,2},{2,2}
%e {2},{2},{1,2,2}
%e {1},{1},{1},{1,1}
%Y First column is A125702. Row sums are A007718.
%Y Cf. A007716, A030019, A052888, A056156, A134954, A147878, A317631, A319557, A320921.
%K nonn,tabl
%O 1,2
%A _Gus Wiseman_, Oct 29 2018
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