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%I #11 Jun 12 2021 12:58:29
%S 0,0,0,0,2,7,19,47,117,284,675,1575,3634,8312,18881,42634,95797,
%T 214376,478110,1063242,2358703,5221606,11538623,25458412,56095424,
%U 123458153,271440387,596277224,1308849869,2871054209,6294182153,13791615999,30206220592,66131277054
%N Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 3.
%H Joerg Arndt and Alois P. Heinz, <a href="/A238914/b238914.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-1,1,-4,-2,-3,-1,1,1,1).
%F G.f.: (x^3-x-2)*x^4 / ((x+1) *(x^6-x^5+x^4-3*x^3+3*x^2-3*x+1) *(x^4+x^3+x^2+x-1)).
%e a(4) = 2: 4231, 4321.
%e a(5) = 7: 15342, 15432, 35142, 42315, 42513, 43215, 45312.
%e a(6) = 19: 126453, 126543, 146253, 153426, 153624, 154326, 156423, 216453, 216543, 351426, 351624, 423156, 423165, 425136, 426153, 432156, 432165, 453126, 456123.
%p gf:= (x^3-x-2)*x^4 / ((x+1)*(x^6-x^5+x^4-3*x^3+3*x^2-3*x+1)*
%p (x^4+x^3+x^2+x-1)):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..40);
%t CoefficientList[Series[(x^3 - x - 2) x^4/((x + 1) (x^6 - x^5 + x^4 - 3 x^3 + 3 x^2 - 3 x + 1) (x^4 + x^3 + x^2 + x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 09 2014 *)
%t LinearRecurrence[{3,-1,-1,1,-4,-2,-3,-1,1,1,1},{0,0,0,0,2,7,19,47,117,284,675},40] (* _Harvey P. Dale_, Jun 12 2021 *)
%Y Column k=3 of A238889.
%K nonn
%O 0,5
%A _Joerg Arndt_ and _Alois P. Heinz_, Mar 07 2014
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