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A076864 Number of connected loopless multigraphs with n edges.

%I A076864 #42 Mar 22 2024 11:06:06
%S A076864 1,1,2,5,12,33,103,333,1183,4442,17576,72810,314595,1410139,6541959,
%T A076864 31322474,154468852,783240943,4077445511,21765312779,118999764062,
%U A076864 665739100725,3807640240209,22246105114743,132672322938379,807126762251748
%N A076864 Number of connected loopless multigraphs with n edges.
%C A076864 Inverse Euler transform of A050535.
%H A076864 Andrew Howroyd, <a href="/A076864/b076864.txt">Table of n, a(n) for n = 0..50</a>
%H A076864 Patrick T. Komiske, Eric M. Metodiev, and Jesse Thaler, <a href="https://arxiv.org/abs/1712.07124">Energy flow polynomials: A complete linear basis for jet substructure</a>, arXiv:1712.07124 [hep-ph], 2017.
%H A076864 Tsuyoshi Miezaki, Akihiro Munemasa, Yusaku Nishimura, Tadashi Sakuma, and Shuhei Tsujie, <a href="https://arxiv.org/abs/2403.09985">Universal graph series, chromatic functions, and their index theory</a>, arXiv:2403.09985 [math.CO], 2024. See p. 23.
%H A076864 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A076864 Gus Wiseman, <a href="/A076864/a076864.png">Non-isomorphic representatives of the unlabeled connected multigraphs counted by the first 5 terms</a>
%t A076864 A050535 = Cases[Import["https://oeis.org/A050535/b050535.txt", "Table"], {_, _}][[All, 2]];
%t A076864 (* EulerInvTransform is defined in A022562 *)
%t A076864 Join[{1}, EulerInvTransform[A050535 // Rest]] (* Jean-François Alcover, Feb 11 2020, updated Mar 17 2020 *)
%Y A076864 Row sums of A191646.
%Y A076864 Cf. A050535 (multisets), A076865, A076866, A076867.
%Y A076864 Cf. A000664, A007718, A054923, A191970, A275421, A317672, A322114, A322137, A322148.
%K A076864 nonn,easy
%O A076864 0,3
%A A076864 _N. J. A. Sloane_, Nov 23 2002
%E A076864 More terms from _Sean A. Irvine_, Oct 02 2011
%E A076864 Name and comment swapped by _Gus Wiseman_, Nov 28 2018
%E A076864 a(0)=1 prepended by _Andrew Howroyd_, Oct 23 2019