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%I M5045 #29 May 17 2019 16:26:45
%S 1,1,17,117,1413,46389,1211085,47977305,2302999889,137682614769,
%T 9844042388505,832087399629125
%N a(n) = number of special even permutations of 2*n+1.
%C a(n) is the number of even permutations, pi(0),...,pi(2*n), of 0,...,2*n such that pi(0) = 0 and p(k) = k + pi(k) (mod 2*n+1), k=0,...,2*n is also a permutation of 0,...,2*n. - _Sean A. Irvine_, Jan 30 2015
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H D. H. Lehmer, <a href="http://dx.doi.org/10.1016/0022-314X(73)90056-5">Some properties of circulants</a>, J. Number Theory 5 (1973), 43-54.
%Y Cf. A003110 (special odd permutations), A003111 (total).
%K nonn,more
%O 1,3
%A _N. J. A. Sloane_
%E a(8)-a(9) from _Sean A. Irvine_, Jan 31 2015
%E a(10)-a(12) from _Vaclav Kotesovec_, May 17 2019 (using the terms of A003111 and A003112)