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%I #21 May 21 2020 12:46:15
%S 0,1,2,4,7,13,23,41,77,149,397,1246,21135,430933,51156773,3044120326,
%T 1704554902881,446193132548644,650868899188542416,
%U 431014163502227412545,2886915606822315071638459,8841362446647790021087061250,152946959203764346079534774815394,1208238394473886999896406262410758886
%N Number of disconnected simple graphs on n vertices with each component regular.
%F a(n) = A165647(n) - A005177(n)
%F = Euler_transformation(A005177)(n) - A005177(n).
%e 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.
%t A005177 = Cases[Import["https://oeis.org/A005177/b005177.txt", "Table"], {_, _}][[All, 2]]~Join~{0};
%t etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b];
%t b = etr[A005177[[# + 1]]&];
%t a[n_] := b[n] - A005177[[n + 1]];
%t a /@ Range[17] (* _Jean-François Alcover_, Dec 02 2019 *)
%Y Cf. A005177, A165647.
%K nonn,hard
%O 1,3
%A _Jason Kimberley_, Sep 23 2009
%E Terms a(18) and beyond from _Andrew Howroyd_, May 21 2020
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