A054944 - OEIS

%I #19 Aug 30 2019 03:44:01

%S 1,1,10,806,282552,367387448,1761545808144,31759604694834608,

%T 2200205489188051324800,595216852658907342647881088,

%U 635231932478914399659212340198144,2690533983413127566229805840755699623168,45382894419701545228622064475653706686181248000,3054532231410772852023213016232868881612380320979954688

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

%H V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LISK/Derseq.html">Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), #00.2.2.

%F a(n) = (A003030(n)+(n-1)!)/2.

%t 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}]];

%t c[1] = 1; c[n_] := c[n] = b[n] + Sum[Binomial[n - 1, j - 1]*b[n - j]*c[j], {j, 1, n - 1}];

%t a[n_] := (c[n] + (n - 1)!)/2;

%t Table[a[n], {n, 1, 15}] (* _Jean-François Alcover_, Aug 30 2019, after _Vaclav Kotesovec_ in A003030 *)

%Y Cf. A054945.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, May 24 2000

%E More terms from _Vladeta Jovovic_, Jul 15 2000

%E More terms from _Jean-François Alcover_, Aug 30 2019