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

Author

N. J. A. Sloane, May 24 2000

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A003030, A054944.

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