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%I M3006 #28 Jun 03 2022 17:54:31
%S 1,1,3,15,138,2021,43581,1295493,50752145,2533755933,157055247261,
%T 11836611005031,1066129321651668,113117849882149725,
%U 13965580274228976213,1985189312618723797371,321932406123733248625851,59079829666712346141491403,12182062872168618012045410805
%N Number of 4-valent labeled graphs with n nodes where multiple edges and loops are allowed.
%C Each loop contributes 2 to the valency of its node.
%D Goulden, I. P.; Jackson, D. M.; Reilly, J. W.; The Hammond series of a symmetric function and its application to P-recursiveness. SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 179-193.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A005816/b005816.txt">Table of n, a(n) for n = 0..50</a> (terms 0..25 from Jason Kimberley)
%H R. C. Read, <a href="http://dx.doi.org/10.1112/jlms/s1-34.4.417">The enumeration of locally restricted graphs (I)</a>, J. London Math. Soc. 34 (1959) 417-436.
%F a(n) = N{E_n[S_4] * S_{2n}[S_2]}.
%Y Column k=4 of A333467.
%Y Cf. A005815.
%Y Cf. A129429 (unlabeled), A033301.
%K nonn
%O 0,3
%A _Simon Plouffe_
%E Definition corrected by appending "where multiple edges and loops are allowed", reference to Read 1959, formula from Read 1959 (5.11), and new terms a(16), a(17), a(18) contributed by _Jason Kimberley_, Jan 22 2010