A007718 - OEIS

%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