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%I #27 Feb 21 2019 15:01:48
%S 1,1,1,2,5,21,117,792,6205,55005,543597,5922930,70518905,910711193,
%T 12678337945,189252400480,3015217932073,51067619064873,
%U 916176426422089,17355904144773970,346195850534379613,7252654441500887309
%N Number of permutations p of {1,2,...,n} such that |p(i)-i| != 1 for all i.
%C For positive n, a(n) equals the permanent of the n X n matrix with 0's along the superdiagonal and the subdiagonal, and 1's everywhere else. [_John M. Campbell_, Jul 09 2011]
%H Vincenzo Librandi, <a href="/A078480/b078480.txt">Table of n, a(n) for n = 0..200</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 223.
%H N. S. Mendelsohn, <a href="http://dx.doi.org/10.4153/CJM-1956-027-7">The asymptotic series for a certain class of permutation problems</a>, Canadian Journal of Mathematics, vol. VIII, No.2, 1956, p.238 (Example 5).
%F G.f.: 1/(1-x^2)*Sum_{n>=0} n!*(x/(1+x)^2)^n. - _Vladeta Jovovic_, Jun 26 2007
%F Asymptotic (N. S. Mendelsohn, 1956): a(n)/n! -> 1/e^2
%F Recurrence: a(n) = n*a(n-1) - (n-2)*a(n-3) - a(n-4), for n>=5
%t (* Explicit formula: *) Table[Sum[Sum[(-1)^k*(i-k)!*Binomial[2i-k,k],{k,0,i}],{i,0,n}],{n,0,21}] (* _Vaclav Kotesovec_, Mar 28 2011 *)
%Y Cf. A000179, A000271.
%Y Column k=0 of A320582.
%Y Column k=1 of A306512.
%K easy,nonn
%O 0,4
%A _Vladeta Jovovic_, Jan 03 2003
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