The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A280088 A151503 A319789 * A297972 A275057 A320807
KEYWORD
nonn
AUTHOR
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 15:59 EDT 2024. Contains 372664 sequences. (Running on oeis4.)