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%I #17 Jan 19 2024 04:32:34
%S 1,7,295,33251,7319436,2669857476,1459913038884,1118904543734724,
%T 1145415466062268695,1510492370204314777345,2494718462461802382223714
%N a(n) = A006690(n)/n^3.
%D Valery A. Liskovets, The number of initially connected automata, Kibernetika, (Kiev), No3 (1969), 16-19; Engl. transl.: Cybernetics, v.4 (1969), 259-262.
%H Valery A. Liskovets, <a href="http://www-igm.univ-mlv.fr/~fpsac/FPSAC03/ARTICLES/5.pdf">Exact enumeration of acyclic automata</a>, Proc. 15th Conf. "Formal Power Series and Algebr. Combin. (FPSAC'03)", 2003.
%H Valery A. Liskovets, <a href="http://dx.doi.org/10.1016/j.dam.2005.06.009">Exact enumeration of acyclic deterministic automata</a>, Discrete Appl. Math., 154, No.3 (2006), 537-551.
%F a(n) := A006690(n)/n^3
%t b[1] = 1; b[n_] := b[n] = n^(3n)/(n-1)! - Sum[n^(3(n-i)) b[i]/(n-i)!, {i, 1, n-1}];
%t a[n_] := b[n]/n^3;
%t Array[a, 11] (* _Jean-François Alcover_, Aug 28 2019 *)
%Y Cf. A006690.
%K easy,nonn
%O 1,2
%A _Valery A. Liskovets_, Apr 09 2003