%I M1225
%S 1,1,1,2,4,10,28,127,686,4975,42529,420948,4622509,55670332,726738971,
%T 10217376792,153848448652,2470073249960,42120966152815,
%U 760282326662191,14481561464994821,290289454462745374,6108699653117045614
%N Permutation arrays of period n.
%C Also superpositions of cycles of order n of the groups S_2 and D_n.  _Sean A. Irvine_, Oct 25 2017
%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 171.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A. P. Street and R. Day, Sequential binary arrays II: Further results on the square grid, pp. 392418 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. OatesWilliams and A. P. Street. Lecture Notes Math., 952. SpringerVerlag, 1982.
%H M. Engelhardt, <a href="/A006841/a006841.txt">Java program</a>
%H V. Meally, <a href="/A003223/a003223.pdf">Letter to N. J. A. Sloane, Feb 1975</a>
%H E. M. Palmer and R. W. Robinson, <a href="http://dx.doi.org/10.1007/BF02392038">Enumeration under two representations of the wreath product</a>, Acta Math., 131 (1973), 123143. (See Table 2, but note errors.)
%H A. P. Street and R. Day, <a href="/A006841/a006841.pdf">Sequential binary arrays II: Further results on the square grid</a>, pp. 392418 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. OatesWilliams and A. P. Street. Lecture Notes Math., 952. SpringerVerlag, 1982. (Annotated scanned copy)
%H Venta Terauds, J. Sumner, <a href="https://arxiv.org/abs/1712.00858">Circular genome rearrangement models: applying representation theory to evolutionary distance calculations</a>, arXiv preprint arXiv:1712.00858 [qbio.PE], 2017.
%F Asymptotic behavior: The nth term T(n) is always larger than n! / (8*n^2) = (n1)! / 8n; for large n, it is approximated by that value. Stated as formula: T(n) > (n1)! / 8n; lim 8n * T(n) / (n1) = 1 as n tends to infinity.
%Y Cf. A061417.
%K nonn,nice
%O 1,4
%A _N. J. A. Sloane_
%E Terms for n=1..8 from A. P. Street and R. Day; other terms computed by _Matthias Engelhardt_. For n=9..12, he used a program which shifts, rotates and mirrors permutations. Terms for n=13..29 computed with a Java program implementing the formulas.
