A003083 - OEIS

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A003083

Sum a(n) x^n / n = log (1 + Sum g(n) x^n ), where g(n) is # graphs on n nodes (A000088).
(Formerly M2691)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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).

LINKS

Table of n, a(n) for n=1..18.

FORMULA

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

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 *)

CROSSREFS

Cf. A000088, A001349.

Sequence in context: A260464 A346658 A246313 * A347639 A350751 A062795

Adjacent sequences: A003080 A003081 A003082 * A003084 A003085 A003086

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved