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%I #9 Jul 28 2024 23:05:28
%S 1,1,0,4,0,0,80,48,0,3328,1920,0,270080,131328,0,3257736,16379904,0,
%T 5750476800,2942582784,0,1376249266176,706948005888,0,430415593603072
%N Number of complete mappings f(x) of Z_{2n+1} such that -(-id+f)^(-1)=f.
%C A complete mapping of a cyclic group (Zn,+) is a permutation f(x) of Zn such that f(0)=0 and that f(x)-x is also a permutation.
%D Y. P. Shieh, "Partition strategies for #P-complete problems with applications to enumerative combinatorics", PhD thesis, National Taiwan University, 2001.
%D Y. P. Shieh, J. Hsiang and D. F. Hsu, "On the enumeration of Abelian k-complete mappings", vol. 144 of Congressus Numerantium, 2000, pp. 67-88.
%H Y. P. Shieh, <a href="http://turing.csie.ntu.edu.tw/~arping/cm">Cyclic complete mappings counting problems</a>
%e f(x)=3x in (Z_7,+) is a complete mapping of Z_7 since f(0)=0 and f(x)-x (=2x) is also a permutation of Z_7. And -(-id+f)^(-1)(x)=f(x).
%Y Cf. A003111.
%K nonn
%O 0,4
%A J. Hsiang, D. F. Hsu and Y. P. Shieh (arping(AT)turing.csie.ntu.edu.tw), Jun 03 2002