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

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;
Table[a[n], {n, 1, 15}] (* Jean-François Alcover, Aug 30 2019, after Vaclav Kotesovec in A003030 *)

Crossrefs

Cf. A054945.

Sequence in context: A211913 A347845 A006440 * A272854 A015093 A104906

Adjacent sequences: A054941 A054942 A054943 * A054945 A054946 A054947

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