A007718 - OEIS

A007718

Number of independent polynomial invariants of matrix of order n.

115

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

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OFFSET

0,3

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

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

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}} {{1,2,3}} {{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

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

STATUS

approved