A054943 Number of connected oriented graphs on n nodes with an odd number of edges.

0, 2, 8, 320, 27584, 6991360, 5179178368, 11396324458496, 74944172892993536, 1476405354971707604992, 87208352627656970712229888, 15450530398306943408625302896640, 8211400756816955708062672318337859584

Offset: 1

Author

N. J. A. Sloane, May 24 2000

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Crossrefs

Cf. A000831, A054941, A054942.

Programs

Mathematica

nn = 15; g[z] :=Sum[(1 + 2 u)^Binomial[n, 2] z^n/n!, {n, 0, nn}]; Drop[
Map[Total[#[[2 ;; Binomial[nn, 2] + 1 ;;2]]]&,Range[0,nn]!CoefficientList[
Series[Log[g[z]], {z, 0, nn}], {z, u}]], 1] (* Geoffrey Critzer, Jul 28 2016 *)

PARI

seq(n)={my(A=O(x*x^n)); Vec(serlaplace(log(sum(k=0, n, 3^binomial(k, 2)*x^k/k!) + A) - log(cos(x + A) + sin(x + A)))/2, -n)} \\ Andrew Howroyd, Sep 10 2018

Formula

a(n) = (A054941(n) + (-1)^n*A000831(n-1))/2. - Andrew Howroyd, Sep 10 2018

Extensions

More terms from Vladeta Jovovic, Mar 11 2003