A054940 - OEIS

A054940

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

0, 1, 1, 22, 352, 13412, 932768, 125776816, 33148125376, 17248244478848, 17820828772662272, 36677298103403269504, 150636101324831804975104, 1235824405515221870758956032, 20263840468865240117261288526848, 664289479167891600504170147259897856

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

OFFSET

1,4

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*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[#[[2 ;; Binomial[nn, 2] ;; 2]]] &, Range[0, nn]! CoefficientList[Series[ Log[f[z]] , {z, 0, nn}], {z, u}]], 1] (* Geoffrey Critzer, Jul 27 2016 *)

CROSSREFS

Cf. A054939.

Sequence in context: A100904 A036738 A332855 * A016265 A208458 A016263

Adjacent sequences: A054937 A054938 A054939 * A054941 A054942 A054943

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 24 2000

EXTENSIONS

More terms from Vladeta Jovovic, Jul 17 2000

STATUS

approved