A003083 Sum a(n) x^n / n = log (1 + Sum g(n) x^n ), where g(n) is # graphs on n nodes (A000088).

1, 3, 7, 27, 106, 681, 5972, 88963, 2349727, 117165818, 11073706216, 1968717966417, 654366802299848, 406048824479878828, 470960717141418629512, 1023512961811602818909395, 4179821138595428450831985657, 32171971054480183600023612728841

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 91.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A000088, A001349.

Programs

Mathematica

nn=20;g=Sum[NumberOfGraphs[n]x^n,{n,1,nn}];Drop[Range[0,nn]CoefficientList[ Series[Log[1+g],{x,0,nn}],x],1]  (* Geoffrey Critzer, Oct 20 2012 *)

Formula

a(n) = Sum_{d|n} d * A001349(d). - Andrey Zabolotskiy, Aug 11 2020