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A054944

Number of strongly connected labeled digraphs on n nodes with an even number of edges.

1, 1, 10, 806, 282552, 367387448, 1761545808144, 31759604694834608, 2200205489188051324800, 595216852658907342647881088, 635231932478914399659212340198144, 2690533983413127566229805840755699623168, 45382894419701545228622064475653706686181248000, 3054532231410772852023213016232868881612380320979954688

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..14.

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;