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

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

Offset

1,2

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

Table of n, a(n) for n=1..11.

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.

Formula

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

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 *)

Crossrefs

Cf. A006690.

Sequence in context: A137435 A220241 A041851 * A362658 A096348 A281435

Adjacent sequences: A082165 A082166 A082167 * A082169 A082170 A082171

Keyword

easy,nonn

Author

Valery A. Liskovets, Apr 09 2003

Status

approved