A165647 Number of simple graphs on n vertices with each component regular.

1, 2, 3, 6, 9, 18, 27, 58, 99, 316, 936, 20225, 410571, 50745729, 2993355213, 1701561156737, 444491521018441, 650424404724148930, 430363737398835017296, 2886485242642120438501318, 8838475960755164592843156768, 152938120727373876718042362054465

Offset: 1

Author

Jason Kimberley, Sep 23 2009

Keywords

• nonn
• hard

Examples

			The a(1)=1 graph is: K_1.
The a(2)=2 graphs are: 2K_1, K_2.
The a(3)=3 graphs are: 3K_1, K_1+K_2, K_3.
The a(4)=6 graphs are: 4K_1, 2K_1+K_2, K_1+K_3, 2K_2, C_4, K_4.
		

Links

• N. J. A. Sloane, Transforms

Crossrefs

Row sums of A275420.

Programs

Mathematica

A005177 = Cases[Import["https://oeis.org/A005177/b005177.txt", "Table"], {, }][[All, 2]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[DivisorSum[j, # p[#]&] b[n - j], {j, 1, n}]/n]; b];
a = etr[A005177[[#+1]]&];
a /@ Range[16] (* Jean-François Alcover, Dec 02 2019 *)

Formula

This sequence is the Euler transformation of A005177.

a(n) = A005177(n) + A165648(n).

Extensions

Terms a(17) and beyond from Andrew Howroyd, May 20 2020