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%I M3169 N1285 #43 Mar 08 2021 22:29:17
%S 3,70,3783,338475,40565585,6061961733,1083852977811,225615988054171,
%T 53595807366038234,14308700593468127485,4241390625289880226714,
%U 1382214286200071777573643,491197439886557439295166226,189044982636675290371386547592,78334771617452038208125184627931,34771576300926271400714044414858372
%N Finite automata.
%C Given the name of A054747, another name for this sequence can be "Number of inequivalent n-state 2-input 2-output connected automata with respect to an input permutation." - _Petros Hadjicostas_, Mar 08 2021
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Christian G. Bower, <a href="https://oeis.org/transforms_pari.txt">PARI programs for transforms</a>, 2007.
%H Michael A. Harrison, <a href="http://dx.doi.org/10.4153/CJM-1965-010-9">A census of finite automata</a>, Canad. J. Math., 17, No. 1, (1965), 100-113. [First apply Theorem 6.2 (p. 107) with k = p = 2 to get A054747. Then apply Theorem 7.2 (p. 110) to get the number of classes of connected automata counted by A054747. - _Petros Hadjicostas_, Mar 08 2021]
%H N. J. A. Sloane, <a href="https://oeis.org/transforms.txt">Maple programs for transforms</a>, 2001-2020.
%F Inverse Euler transform of A054747. - _Petros Hadjicostas_, Mar 08 2021
%o (PARI) /* This program is a modification of _Christian G. Bower_'s PARI program for the inverse Euler transform from the link above. */
%o lista(nn) = {local(A=vector(nn+1)); for(n=1, nn+1, A[n]=if(n==1, 1, A054747(n-1))); local(B=vector(#A-1,n,1/n),C); A[1] = 1; C = log(Ser(A)); A=vecextract(A,"2.."); for(i=1, #A, A[i] = polcoeff(C,i)); A = dirdiv(A,B); } \\ _Petros Hadjicostas_, Mar 08 2021
%Y Cf. A002854, A054732, A054747.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Apr 22 2000
%E Terms a(14)-a(16) from _Petros Hadjicostas_, Mar 08 2021
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