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%I #18 Aug 27 2019 10:53:26
%S 0,1,3,76,8220,3418216,5156362008,28205998918336,571801003320734400,
%T 44006976469834509225856,13095012982298536065778624128,
%U 15245644966564725709168192019570176,69953982671396722666217758540260522923520,1270721533437616701720124856867026526491583190016
%N Number of labeled semi-strong digraphs on n nodes with an even number of components.
%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) = (A054948(n) - A054947(n))/2. - _Andrew Howroyd_, Sep 10 2018
%t A054947[1] = 1; A054947[n_] := A054947[n] = 2^(n (n - 1)) - Sum[Binomial[n, j] 2^((n - 1) (n - j)) A054947[j], {j, 1, n - 1}];
%t A054948[0] = 1; A054948[n_] := A054948[n] = Module[{A}, A = 1 + Sum[ A054948[k]*x^k/k!, {k, 1, n - 1}]; n!*SeriesCoefficient[Sum[2^(k^2 - k)*x^k/k!/(A /. x -> 2^k*x) , {k, 0, n}], {x, 0, n}]];
%t a[n_] := (A054948[n] - A054947[n])/2;
%t Array[a, 14] (* _Jean-François Alcover_, Aug 27 2019 *)
%Y Cf. A054947, A054948, A054949.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, May 24 2000
%E More terms from _Vladeta Jovovic_, Mar 11 2003
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