

A071608


Number of complete mappings f(x) of Z_{2n+1} such that (id+f)^(1)=f.


2



1, 1, 0, 4, 0, 0, 80, 48, 0, 3328, 1920, 0, 270080, 131328, 0, 3257736, 16379904, 0, 5750476800, 2942582784, 0, 1376249266176, 706948005888, 0, 430415593603072
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OFFSET

0,4


COMMENTS

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.


REFERENCES

Y. P. Shieh, "Partition strategies for #Pcomplete problems with applications to enumerative combinatorics", PhD thesis, National Taiwan University, 2001.
Y. P. Shieh, J. Hsiang and D. F. Hsu, "On the enumeration of Abelian kcomplete mappings", vol. 144 of Congressus Numerantium, 2000, pp. 6788.


LINKS

Table of n, a(n) for n=0..24.
Y. P. Shieh, Cyclic complete mappings counting problems


EXAMPLE

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).


CROSSREFS

Sequence in context: A054376 A351156 A358292 * A013451 A013462 A326862
Adjacent sequences: A071605 A071606 A071607 * A071609 A071610 A071611


KEYWORD

nonn


AUTHOR

J. Hsiang, D. F. Hsu and Y. P. Shieh (arping(AT)turing.csie.ntu.edu.tw), Jun 03 2002


STATUS

approved



