This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A027835 #43 Jul 08 2025 17:55:32
%S A027835 1,6,52,892,21291,658885,24617866,1077142765,53918557215,
%T A027835 3036369842197,189881640057942,13051044976503663,977672716919010876,
%U A027835 79267586388173032966,6914956215333832011058,645771787789692953182732,64277686448923785217048191,6793045601578652098886514581,759656437858515775195264228768,89619947709601175930862298926038
%N A027835 Number of unlabeled strongly connected n-state 2-input automata.
%H A027835 Michael A. Harrison, <a href="https://doi.org/10.4153/CJM-1965-010-9">A census of finite automata</a>, Canadian Journal of Mathematics, 17 (1965), 100-113.
%H A027835 Valery A. Liskovets [ Liskovec ], <a href="https://www.researchgate.net/publication/268532943_Enumeration_of_non-isomorphic_strongly_connected_automata">Enumeration of nonisomorphic strongly connected automata</a>, (in Russian); Vesti Akad. Nauk. Belarus. SSR, Ser. Phys.-Mat., No. 3, 1971, pp. 26-30, esp. p. 30 (Math. Rev. 46 #5081; <a href="https://www.zbmath.org/?q=an%3A0224.94053">Zentralblatt 224 #94053</a>).
%H A027835 Valery A. Liskovets [ Liskovec ], <a href="https://www.researchgate.net/publication/246994823_ON_A_GENERAL_ENUMERATIVE_SCHEME_FOR_LABELED_GRAPHS">A general enumeration scheme for labeled graphs</a>, (in Russian); Dokl. Akad. Nauk. Belarus. SSR, Vol. 21, No. 6 (1977), pp. 496-499 (Math. Rev. 58 #21797; <a href="https://www.zbmath.org/?q=an%3A0412.05052">Zentralblatt 412 #05052</a>).
%o A027835 (PARI) {v(r, n) = if(n==0, 1, n^(r*n) - sum(t=1, n-1, binomial(n, t) * n^(r*(n-t)) * v(r, t) ))}
%o A027835 {s(r, n) = v(r, n) + sum(t=1, n-1, binomial(n-1, t-1) * v(r, n-t) * s(r, t) )} \\ This is _Paul D. Hanna_'s PARI program from A027834 regarding s(r,n) = number of labeled strongly connected n-state r-input automata.
%o A027835 {SS(r,n) = (1/n)*sumdiv(n, m, (s(r,m)/(m-1)!)*sumdiv(n/m, d, moebius(n/(m*d))*d^((r-1)*m+1)))} \\ This calculates the number of unlabeled strongly connected n-state r-input automata. It is _Valery A. Liskovets_'s formula from his 1971 paper.
%o A027835 for(n=1, 20, print1( SS(r=2, n), ", ")) \\ _Petros Hadjicostas_, Feb 26 2021
%Y A027835 Cf. A006689, A027834.
%K A027835 nonn
%O A027835 1,2
%A A027835 _N. J. A. Sloane_
%E A027835 More terms from _Petros Hadjicostas_, Feb 26 2021 using formula (5), p. 28, in Liskovets (1971)