VOOZH about

URL: https://oeis.org/A054950

⇱ A054950 - OEIS

login
A054950
Number of labeled semi-strong digraphs on n nodes with an even number of components.
1
0, 1, 3, 76, 8220, 3418216, 5156362008, 28205998918336, 571801003320734400, 44006976469834509225856, 13095012982298536065778624128, 15245644966564725709168192019570176, 69953982671396722666217758540260522923520, 1270721533437616701720124856867026526491583190016
OFFSET
1,3
LINKS
V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.
FORMULA
a(n) = (A054948(n) - A054947(n))/2. - Andrew Howroyd, Sep 10 2018
MATHEMATICA
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}];
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}]];
a[n_] := (A054948[n] - A054947[n])/2;
Array[a, 14] (* Jean-François Alcover, Aug 27 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 24 2000
EXTENSIONS
More terms from Vladeta Jovovic, Mar 11 2003
STATUS
approved