A054945 Number of strongly connected labeled digraphs on n nodes with an odd number of edges.
0, 0, 8, 800, 282528, 367387328, 1761545807424, 31759604694829568, 2200205489188051284480, 595216852658907342647518208, 635231932478914399659212336569344, 2690533983413127566229805840755659706368, 45382894419701545228622064475653706685702246400, 3054532231410772852023213016232868881612380314752933888
Offset: 1
Links
- V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
Programs
-
Mathematica
b[n_] := b[n] = If[n == 1, 1, 2^(n*(n - 1)) - Sum[Binomial[n, j]*2^((n - 1)*(n - j))*b[j], {j, 1, n - 1}]]; c[1] = 1; c[n_] := c[n] = b[n] + Sum[Binomial[n - 1, j - 1]*b[n - j]*c[j], {j, 1, n - 1}]; a[n_] := (c[n] - (n - 1)!)/2; Table[a[n], {n, 1, 15}] (* Jean-François Alcover, Aug 30 2019, after Vaclav Kotesovec in A003030 *)
Formula
a(n) = (A003030(n)-(n-1)!)/2.
Extensions
More terms from Vladeta Jovovic, Jul 15 2000
More terms from Jean-François Alcover, Aug 30 2019