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 A300913 Number of non-isomorphic connected set-systems of weight n. 34
 1, 1, 1, 2, 4, 7, 18, 37, 96, 239, 658, 1810, 5358, 16057, 50373, 161811, 536964, 1826151, 6380481, 22822280, 83587920, 312954111, 1197178941, 4674642341, 18620255306, 75606404857, 312763294254, 1317356836235, 5646694922172, 24618969819915, 109125629486233, 491554330852608 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The weight of a set-system is the sum of cardinalities of the sets. Weight is generally not the same as number of vertices. LINKS Jean-François Alcover, Table of n, a(n) for n = 0..50 [using Andrew Howroyd's b-file for A283877] FORMULA Inverse Euler transform of A283877. EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems: 1: {{1}} 2: {{1,2}} 3: {{1,2,3}}    {{2},{1,2}} 4: {{1,2,3,4}}    {{3},{1,2,3}}    {{1,3},{2,3}}    {{1},{2},{1,2}} 5: {{1,2,3,4,5}}    {{4},{1,2,3,4}}    {{1,4},{2,3,4}}    {{2,3},{1,2,3}}    {{2},{3},{1,2,3}}    {{2},{1,3},{2,3}}    {{3},{1,3},{2,3}} Non-isomorphic representatives of the a(6) = 18 connected set-systems:   {{1,2,3,4,5,6}}   {{5},{1,2,3,4,5}}   {{1,5},{2,3,4,5}}   {{3,4},{1,2,3,4}}   {{1,2,5},{3,4,5}}   {{1,3,4},{2,3,4}}   {{1},{1,4},{2,3,4}}   {{1},{2,3},{1,2,3}}   {{3},{4},{1,2,3,4}}   {{3},{1,4},{2,3,4}}   {{3},{2,3},{1,2,3}}   {{4},{1,4},{2,3,4}}   {{1,2},{1,3},{2,3}}   {{1,3},{2,4},{3,4}}   {{1,4},{2,4},{3,4}}   {{1},{2},{3},{1,2,3}}   {{1},{2},{1,3},{2,3}}   {{2},{3},{1,3},{2,3}} MATHEMATICA A283877 = Import["https://oeis.org/A283877/b283877.txt", "Table"][[All, 2]]; (* EulerInvTransform is defined in A022562 *) {1} ~Join~ EulerInvTransform[A283877 // Rest] (* Jean-François Alcover, Nov 07 2019, updated Mar 17 2020 *) CROSSREFS Cf. A007716, A055621, A283877, A293606, A293607. Sequence in context: A103032 A215649 A259351 * A232484 A223013 A276027 Adjacent sequences:  A300910 A300911 A300912 * A300914 A300915 A300916 KEYWORD nonn AUTHOR Gus Wiseman, Jun 19 2018 EXTENSIONS a(11)-a(31) from Jean-François Alcover, Nov 07 2019 STATUS approved

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Last modified April 11 19:49 EDT 2021. Contains 342888 sequences. (Running on oeis4.)