%I #33 Mar 18 2020 09:00:38
%S 1,0,0,1,3,60,7849,3459386,2585136741,2807105258926,4221456120848125,
%T 8516994772686533749,22470883220896245217626,
%U 75883288448434648617038134,322040154712674550886226182668
%N Number of 5-regular graphs (quintic graphs) on 2n vertices.
%C Because the triangle A051031 is symmetric, a(n) is also the number of (2n-6)-regular graphs on 2n vertices.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_ge_g_index">Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g</a>
%H M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%H M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199902)30:2<137::AID-JGT7>3.0.CO;2-G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137-146.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Euler transform of A006821.
%t A006821 = Cases[Import["https://oeis.org/A006821/b006821.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerTransform is defined in A005195 *)
%t EulerTransform[Rest @ A006821] (* _Jean-François Alcover_, Dec 04 2019, updated Mar 18 2020 *)
%Y 5-regular simple graphs: A006821 (connected), A165655 (disconnected), this sequence (not necessarily connected).
%Y Regular graphs A005176 (any degree), A051031 (triangular array), specified degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), this sequence (k=5), A165627 (k=6), A165628 (k=7), A180260 (k=8).
%K nonn,hard,more
%O 0,5
%A _Jason Kimberley_, Sep 22 2009
%E Regular graphs cross-references edited by _Jason Kimberley_, Nov 07 2009
%E a(9) from _Jason Kimberley_, Nov 24 2009
%E a(10)-a(14) from _Andrew Howroyd_, Mar 10 2020