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

%I A300913 #26 Mar 17 2020 14:39:13
%S A300913 1,1,1,2,4,7,18,37,96,239,658,1810,5358,16057,50373,161811,536964,
%T A300913 1826151,6380481,22822280,83587920,312954111,1197178941,4674642341,
%U A300913 18620255306,75606404857,312763294254,1317356836235,5646694922172,24618969819915,109125629486233,491554330852608
%N A300913 Number of non-isomorphic connected set-systems of weight n.
%C A300913 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 A300913 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 A300913 Inverse Euler transform of A283877.
%e A300913 Non-isomorphic representatives of the a(1) = 1 through a(5) = 7 set systems:
%e A300913 1: {{1}}
%e A300913 2: {{1,2}}
%e A300913 3: {{1,2,3}}
%e A300913    {{2},{1,2}}
%e A300913 4: {{1,2,3,4}}
%e A300913    {{3},{1,2,3}}
%e A300913    {{1,3},{2,3}}
%e A300913    {{1},{2},{1,2}}
%e A300913 5: {{1,2,3,4,5}}
%e A300913    {{4},{1,2,3,4}}
%e A300913    {{1,4},{2,3,4}}
%e A300913    {{2,3},{1,2,3}}
%e A300913    {{2},{3},{1,2,3}}
%e A300913    {{2},{1,3},{2,3}}
%e A300913    {{3},{1,3},{2,3}}
%e A300913 Non-isomorphic representatives of the a(6) = 18 connected set-systems:
%e A300913   {{1,2,3,4,5,6}}
%e A300913   {{5},{1,2,3,4,5}}
%e A300913   {{1,5},{2,3,4,5}}
%e A300913   {{3,4},{1,2,3,4}}
%e A300913   {{1,2,5},{3,4,5}}
%e A300913   {{1,3,4},{2,3,4}}
%e A300913   {{1},{1,4},{2,3,4}}
%e A300913   {{1},{2,3},{1,2,3}}
%e A300913   {{3},{4},{1,2,3,4}}
%e A300913   {{3},{1,4},{2,3,4}}
%e A300913   {{3},{2,3},{1,2,3}}
%e A300913   {{4},{1,4},{2,3,4}}
%e A300913   {{1,2},{1,3},{2,3}}
%e A300913   {{1,3},{2,4},{3,4}}
%e A300913   {{1,4},{2,4},{3,4}}
%e A300913   {{1},{2},{3},{1,2,3}}
%e A300913   {{1},{2},{1,3},{2,3}}
%e A300913   {{2},{3},{1,3},{2,3}}
%t A300913 A283877 = Import["https://oeis.org/A283877/b283877.txt", "Table"][[All, 2]];
%t A300913 (* EulerInvTransform is defined in A022562 *)
%t A300913 {1} ~Join~ EulerInvTransform[A283877 // Rest] (* _Jean-François Alcover_, Nov 07 2019, updated Mar 17 2020 *)
%Y A300913 Cf. A007716, A055621, A283877, A293606, A293607.
%K A300913 nonn
%O A300913 0,4
%A A300913 _Gus Wiseman_, Jun 19 2018
%E A300913 a(11)-a(31) from _Jean-François Alcover_, Nov 07 2019