A054939 - OEIS

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A054939

Number of connected labeled graphs with n nodes and an even number of edges.

1, 0, 3, 16, 376, 13292, 933488, 125771776, 33148165696, 17248244115968, 17820828776291072, 36677298103363352704, 150636101324832283976704, 1235824405515221864531935232, 20263840468865240117348466818048, 664289479167891600504168839585529856

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

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..16.

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

FORMULA

a(n) = (A001187(n)+(-1)^(n-1)*A000142(n-1))/2.

MATHEMATICA

nn = 15; Clear[f]; f[z_] := Sum[(1 + u)^Binomial[n, 2] z^n/n!, {n, 0, nn + 1}]; Drop[Map[Total[#[[1 ;; Binomial[nn, 2] ;; 2]]] &, Range[0, nn]! CoefficientList[Series[ Log[f[z]] , {z, 0, nn}], {z, u}]], 1] (* Geoffrey Critzer, Jul 27 2016 *)

CROSSREFS

Sequence in context: A005031 A300960 A224440 * A081782 A176299 A081780

Adjacent sequences: A054936 A054937 A054938 * A054940 A054941 A054942

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 24 2000

EXTENSIONS

More terms from Vladeta Jovovic, Jul 17 2000

STATUS

approved