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A054945
Number of strongly connected labeled digraphs on n nodes with an odd number of edges.
1
0, 0, 8, 800, 282528, 367387328, 1761545807424, 31759604694829568, 2200205489188051284480, 595216852658907342647518208, 635231932478914399659212336569344, 2690533983413127566229805840755659706368, 45382894419701545228622064475653706685702246400, 3054532231410772852023213016232868881612380314752933888
OFFSET
1,3
LINKS
V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
FORMULA
a(n) = (A003030(n)-(n-1)!)/2.
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 *)
CROSSREFS
Sequence in context: A001547 A168310 A220186 * A158817 A159707 A097818
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 24 2000
EXTENSIONS
More terms from Vladeta Jovovic, Jul 15 2000
More terms from Jean-François Alcover, Aug 30 2019
STATUS
approved