A007718 Number of independent polynomial invariants of matrix of order n.

1, 1, 3, 6, 17, 40, 125, 354, 1159, 3774, 13113, 46426, 171027, 644038, 2493848, 9867688, 39922991, 164747459, 693093407, 2968918400, 12940917244, 57353242370, 258306634422, 1181572250326, 5486982683756, 25856584485254

Offset: 0

Author

Colin Mallows

Keywords

• nonn

Comments

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

Examples

			From _Gus Wiseman_, Sep 24 2018: (Start)
Non-isomorphic representatives of the a(1) = 1 through a(4) = 17 connected multiset partitions:
  {{1}}  {{1,1}}    {{1,1,1}}      {{1,1,1,1}}
         {{1,2}}    {{1,2,2}}      {{1,1,2,2}}
        {{1},{1}}   {{1,2,3}}      {{1,2,2,2}}
                   {{1},{1,1}}     {{1,2,3,3}}
                   {{2},{1,2}}     {{1,2,3,4}}
                  {{1},{1},{1}}   {{1},{1,1,1}}
                                  {{1},{1,2,2}}
                                  {{2},{1,2,2}}
                                  {{3},{1,2,3}}
                                  {{1,1},{1,1}}
                                  {{1,2},{1,2}}
                                  {{1,2},{2,2}}
                                  {{1,3},{2,3}}
                                 {{1},{1},{1,1}}
                                 {{1},{2},{1,2}}
                                 {{2},{2},{1,2}}
                                {{1},{1},{1},{1}}
(End)
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A007716, A007718, A056156, A319557, A319565, A319566.

Formula

Inverse Euler transform of A007716.

Extensions

a(7)-a(25) from Franklin T. Adams-Watters, Jun 21 2011

a(0)=1 prepended by Andrew Howroyd, Jan 15 2023