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 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 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}} {{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 a(0)=1 prepended by Andrew Howroyd, Jan 15 2023 STATUS approved

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