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%I #22 Feb 09 2024 01:43:48
%S 1,0,1,2,4,9,26,68,217,718,2553,9574,38005,157306,679682,3047699,
%T 14150278,67844305,335262807,1704500229,8902528600,47704608478,
%U 261960998230,1472618327415,8466681788462,49743177379613,298407523833717,1826531247381194,11399711132242500,72500116125222893,469578870456459042
%N Number of unlabeled connected leafless loopless multigraphs with n edges.
%C Connected multigraphs with no loops and no vertices of degree 1.
%C The initial terms were computed with Nauty.
%H Andrew Howroyd, <a href="/A307317/b307317.txt">Table of n, a(n) for n = 0..50</a>
%H P. T. Komiske, E. M. Metodiev, and J. Thaler, <a href="https://arxiv.org/abs/1911.04491">Cutting Multiparticle Correlators Down to Size</a>, arXiv:1911.04491 [hep-ph], 2019-2020.
%H Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it/">nauty and Traces</a>.
%F Inverse Euler transform of A307316.
%e For n=3 the multigraphs (as sets of edges) are {(0,1),(0,1),(0,1)} and {(0,1),(0,2),(1,2)}.
%Y Cf. A076864, A307316 (not necessarily connected), A342556 (simple graphs).
%K nonn
%O 0,4
%A _Eric M. Metodiev_, Apr 02 2019
%E a(0)=1 prepended and a(17) onwards from _Andrew Howroyd_, Feb 01 2024
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