A165648 Number of disconnected simple graphs on n vertices with each component regular.

0, 1, 2, 4, 7, 13, 23, 41, 77, 149, 397, 1246, 21135, 430933, 51156773, 3044120326, 1704554902881, 446193132548644, 650868899188542416, 431014163502227412545, 2886915606822315071638459, 8841362446647790021087061250, 152946959203764346079534774815394, 1208238394473886999896406262410758886

Offset: 1

Author

Jason Kimberley, Sep 23 2009

Keywords

• nonn
• hard

Examples

			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.
		

Crossrefs

Cf. A005177, A165647.

Programs

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 *)

Formula

a(n) = A165647(n) - A005177(n)

= Euler_transformation(A005177)(n) - A005177(n).

Extensions

Terms a(18) and beyond from Andrew Howroyd, May 21 2020