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%I #20 Mar 17 2020 19:31:27
%S 1,1,2,7,53,712,24576,2275616,589543159,420188096140,819411181635025,
%T 4381819315336997184,64583749250393921183423,
%U 2638507778912832094660037006,300397569392490080058575760090548,95776592061550107555640978862165082446
%N Number of connected 2-multigraphs on n nodes.
%C A 2-multigraph is similar to an ordinary graph except there are 0, 1 or 2 edges between any two nodes (self-loops are not allowed).
%C Also the number of connected signed graphs on n unlabeled nodes. - _Andrew Howroyd_, Sep 25 2018
%H Andrew Howroyd, <a href="/A053465/b053465.txt">Table of n, a(n) for n = 0..50</a>
%H Edward A. Bender and E. Rodney Canfield, <a href="https://doi.org/10.1016/0095-8956(83)90040-0">Enumeration of connected invariant graphs</a>, Journal of Combinatorial Theory, Series B 34.3 (1983): 268-278. See p. 273.
%F Inverse Euler transform of A004102. - _Andrew Howroyd_, Sep 25 2018
%t A004102 = Import["https://oeis.org/A004102/b004102.txt", "Table"][[All, 2]];
%t (* EulerInvTransform is defined in A022562 *)
%t Join[{1}, EulerInvTransform[A004102 // Rest]] (* _Jean-François Alcover_, Sep 12 2019, after Andrew Howroyd, updated Mar 17 2020 *)
%Y Cf. A004102, A318590.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Jan 13 2000
%E a(0)=1 prepended and terms a(15) and beyond from _Andrew Howroyd_, Sep 25 2018