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A007718 Number of independent polynomial invariants of matrix of order n. 77
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..25.

FORMULA

Inverse Euler transform of A007716.

EXAMPLE

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)

CROSSREFS

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

Sequence in context: A280088 A151503 A319789 * A297972 A275057 A320807

Adjacent sequences:  A007715 A007716 A007717 * A007719 A007720 A007721

KEYWORD

nonn

AUTHOR

Colin Mallows

EXTENSIONS

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

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)