A082168 a(n) = A006690(n)/n^3.

1, 7, 295, 33251, 7319436, 2669857476, 1459913038884, 1118904543734724, 1145415466062268695, 1510492370204314777345, 2494718462461802382223714

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. A006690.

Programs

Mathematica

b[1] = 1; b[n_] := b[n] = n^(3n)/(n-1)! - Sum[n^(3(n-i)) b[i]/(n-i)!, {i, 1, n-1}];
a[n_] := b[n]/n^3;
Array[a, 11] (* Jean-François Alcover, Aug 28 2019 *)

Formula

a(n) := A006690(n)/n^3