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A300913 Number of non-isomorphic connected set-systems of weight n. 34

%I

%S 1,1,1,2,4,7,18,37,96,239,658,1810,5358,16057,50373,161811,536964,

%T 1826151,6380481,22822280,83587920,312954111,1197178941,4674642341,

%U 18620255306,75606404857,312763294254,1317356836235,5646694922172,24618969819915,109125629486233,491554330852608

%N Number of non-isomorphic connected set-systems of weight n.

%C The weight of a set-system is the sum of cardinalities of the sets. Weight is generally not the same as number of vertices.

%H Jean-François Alcover, <a href="/A300913/b300913.txt">Table of n, a(n) for n = 0..50</a> [using Andrew Howroyd's b-file for A283877]

%F Inverse Euler transform of A283877.

%e Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems:

%e 1: {{1}}

%e 2: {{1,2}}

%e 3: {{1,2,3}}

%e {{2},{1,2}}

%e 4: {{1,2,3,4}}

%e {{3},{1,2,3}}

%e {{1,3},{2,3}}

%e {{1},{2},{1,2}}

%e 5: {{1,2,3,4,5}}

%e {{4},{1,2,3,4}}

%e {{1,4},{2,3,4}}

%e {{2,3},{1,2,3}}

%e {{2},{3},{1,2,3}}

%e {{2},{1,3},{2,3}}

%e {{3},{1,3},{2,3}}

%e Non-isomorphic representatives of the a(6) = 18 connected set-systems:

%e {{1,2,3,4,5,6}}

%e {{5},{1,2,3,4,5}}

%e {{1,5},{2,3,4,5}}

%e {{3,4},{1,2,3,4}}

%e {{1,2,5},{3,4,5}}

%e {{1,3,4},{2,3,4}}

%e {{1},{1,4},{2,3,4}}

%e {{1},{2,3},{1,2,3}}

%e {{3},{4},{1,2,3,4}}

%e {{3},{1,4},{2,3,4}}

%e {{3},{2,3},{1,2,3}}

%e {{4},{1,4},{2,3,4}}

%e {{1,2},{1,3},{2,3}}

%e {{1,3},{2,4},{3,4}}

%e {{1,4},{2,4},{3,4}}

%e {{1},{2},{3},{1,2,3}}

%e {{1},{2},{1,3},{2,3}}

%e {{2},{3},{1,3},{2,3}}

%t A283877 = Import["https://oeis.org/A283877/b283877.txt", "Table"][[All, 2]];

%t (* EulerInvTransform is defined in A022562 *)

%t {1} ~Join~ EulerInvTransform[A283877 // Rest] (* _Jean-François Alcover_, Nov 07 2019, updated Mar 17 2020 *)

%Y Cf. A007716, A055621, A283877, A293606, A293607.

%K nonn

%O 0,4

%A _Gus Wiseman_, Jun 19 2018

%E a(11)-a(31) from _Jean-François Alcover_, Nov 07 2019

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)