A082166 a(n) = A006689(n)/n^2.

1, 3, 24, 328, 6427, 164765, 5228210, 197897582, 8704544263, 436312502297, 24550259053858, 1532241939881294, 105048412352334420, 7847739530288388636, 634523723233529394594, 55206024491463561241758, 5142697402316326354705599, 510704188733699181740089521, 53858874208665420063477867788

Offset: 1

Author

Valery A. Liskovets, Apr 09 2003

Keywords

• easy
• nonn

References

• Valery A. Liskovets, The number of initially connected automata, Kibernetika, (Kiev), No3 (1969), 16-19; Engl. transl.: Cybernetics, v.4 (1969), 259-262.

Links

• Valery A. Liskovets, Exact enumeration of acyclic automata, Proc. 15th Conf. "Formal Power Series and Algebr. Combin. (FPSAC'03)", 2003.
• Valery A. Liskovets, Exact enumeration of acyclic deterministic automata, Discrete Appl. Math., 154, No.3 (2006), 537-551.

Crossrefs

Cf. A006689.

Programs

Mathematica

b[n_] := b[n] = If[n == 1, 1, n^(2*n)/(n-1)! - Sum[n^(2*(n-i))*b[i]/(n-i)!, {i, 1, n-1}]];
a[n_] := b[n]/n^2;
Array[a, 16] (* Jean-François Alcover, Aug 28 2019 *)