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 A165648 Number of disconnected simple graphs on n vertices with each component regular. 2
 0, 1, 2, 4, 7, 13, 23, 41, 77, 149, 397, 1246, 21135, 430933, 51156773, 3044120326, 1704554902881, 446193132548644, 650868899188542416, 431014163502227412545, 2886915606822315071638459, 8841362446647790021087061250, 152946959203764346079534774815394, 1208238394473886999896406262410758886 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA a(n) = A165647(n) - A005177(n)      = Euler_transformation(A005177)(n) - A005177(n). EXAMPLE The a(2)=1 graph is: 2K_1. The a(3)=2 graphs are: 3K_1, K_1+K_2. The a(4)=4 graphs are: 4K_1, 2K_1+K_2, K_1+K_3, 2K_2. MATHEMATICA A005177 = Cases[Import["https://oeis.org/A005177/b005177.txt", "Table"], {_, _}][[All, 2]]~Join~{0}; etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b]; b = etr[A005177[[# + 1]]&]; a[n_] := b[n] - A005177[[n + 1]]; a /@ Range[17] (* Jean-François Alcover, Dec 02 2019 *) CROSSREFS Cf. A005177, A165647. Sequence in context: A003116 A303666 A260917 * A287381 A078038 A190502 Adjacent sequences:  A165645 A165646 A165647 * A165649 A165650 A165651 KEYWORD nonn,hard AUTHOR Jason Kimberley, Sep 23 2009 EXTENSIONS Terms a(18) and beyond from Andrew Howroyd, May 21 2020 STATUS approved

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Last modified August 6 12:33 EDT 2020. Contains 336246 sequences. (Running on oeis4.)