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A008325 Number of simple regular trivalent bipartite graphs with 2n nodes.

%I A008325 #28 Apr 04 2020 11:04:58
%S A008325 1,1,2,6,14,41,157,725,4196,29816,246644,2297075,23503477,260265023,
%T A008325 3090336300,39101547971,524782945991,7443247863498,111221983956652,
%U A008325 1746165682538497,28734206614035245,494526496354065244,8883865784392246280,166286434745252091055,3237719048384605059117,65477287940472122129194
%N A008325 Number of simple regular trivalent bipartite graphs with 2n nodes.
%C A008325 Euler transform of A006823. - _Peter J. Taylor_, Sep 28 2017
%H A008325 G. Brinkmann, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199610)23:2&lt;139::AID-JGT5&gt;3.0.CO;2-U">Fast generation of cubic graphs</a>, Journal of Graph Theory, 23(2):139-149, 1996.
%H A008325 Sean A. Irvine, <a href="/A008325/a008325.png">On the difference between A004066 and A008325</a>
%t A008325 A006823 = Cases[Import["https://oeis.org/A006823/b006823.txt", "Table"], {_, _}][[All, 2]];
%t A008325 etr[f_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d f[d], {d, Divisors[j]}] b[n - j], {j, 1, n}]/n]; b];
%t A008325 b[n_] := If[n >= 3, A006823[[n - 2]], 0];
%t A008325 a = etr[b];
%t A008325 a /@ Range[3, 16] (* _Jean-François Alcover_, Dec 03 2019 *)
%Y A008325 Column k=3 of A008327.
%Y A008325 Cf. A004066 (bicolored), A006823 (connected).
%K A008325 nonn,hard
%O A008325 3,3
%A A008325 _Brendan McKay_
%E A008325 a(15)-a(16) from _Peter J. Taylor_, Sep 28 2017
%E A008325 Terms a(17) and beyond from _Andrew Howroyd_, Apr 03 2020