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%I #18 Jan 15 2023 19:49:25
%S 1,1,3,6,17,40,125,354,1159,3774,13113,46426,171027,644038,2493848,
%T 9867688,39922991,164747459,693093407,2968918400,12940917244,
%U 57353242370,258306634422,1181572250326,5486982683756,25856584485254
%N Number of independent polynomial invariants of matrix of order n.
%C Also the number of non-isomorphic connected multiset partitions of weight n. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. - _Gus Wiseman_, Sep 23 2018
%H Andrew Howroyd, <a href="/A007718/b007718.txt">Table of n, a(n) for n = 0..50</a>
%F Inverse Euler transform of A007716.
%e From _Gus Wiseman_, Sep 24 2018: (Start)
%e Non-isomorphic representatives of the a(1) = 1 through a(4) = 17 connected multiset partitions:
%e {{1}} {{1,1}} {{1,1,1}} {{1,1,1,1}}
%e {{1,2}} {{1,2,2}} {{1,1,2,2}}
%e {{1},{1}} {{1,2,3}} {{1,2,2,2}}
%e {{1},{1,1}} {{1,2,3,3}}
%e {{2},{1,2}} {{1,2,3,4}}
%e {{1},{1},{1}} {{1},{1,1,1}}
%e {{1},{1,2,2}}
%e {{2},{1,2,2}}
%e {{3},{1,2,3}}
%e {{1,1},{1,1}}
%e {{1,2},{1,2}}
%e {{1,2},{2,2}}
%e {{1,3},{2,3}}
%e {{1},{1},{1,1}}
%e {{1},{2},{1,2}}
%e {{2},{2},{1,2}}
%e {{1},{1},{1},{1}}
%e (End)
%Y Cf. A007716, A007718, A056156, A319557, A319565, A319566.
%K nonn
%O 0,3
%A _Colin Mallows_
%E a(7)-a(25) from _Franklin T. Adams-Watters_, Jun 21 2011
%E a(0)=1 prepended by _Andrew Howroyd_, Jan 15 2023
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