A054950 Number of labeled semi-strong digraphs on n nodes with an even number of components.

0, 1, 3, 76, 8220, 3418216, 5156362008, 28205998918336, 571801003320734400, 44006976469834509225856, 13095012982298536065778624128, 15245644966564725709168192019570176, 69953982671396722666217758540260522923520, 1270721533437616701720124856867026526491583190016

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) = (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

Cf. A054947, A054948, A054949.

Sequence in context: A054747 A302375 A232030 * A335722 A183961 A250328

Adjacent sequences: A054947 A054948 A054949 * A054951 A054952 A054953

Keyword

nonn,easy

Author

N. J. A. Sloane, May 24 2000

Extensions

More terms from Vladeta Jovovic, Mar 11 2003

Status

approved