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A239077 Number of self-inverse permutations p on [n] with displacement of elements restricted by 5: |p(i)-i| <= 5.

%I A239077 #10 Mar 12 2014 08:02:06
%S A239077 1,1,2,4,10,26,76,206,546,1406,3608,9259,23981,62324,162224,422028,
%T A239077 1096900,2848240,7394076,19196044,49844356,129443736,336182997,
%U A239077 873106045,2267493182,5888625652,15292437454,39713590230,103134439084,267836774530,695564961926
%N A239077 Number of self-inverse permutations p on [n] with displacement of elements restricted by 5: |p(i)-i| <= 5.
%C A239077 Column k=5 of A238888.
%H A239077 Joerg Arndt and Alois P. Heinz, <a href="/A239077/b239077.txt">Table of n, a(n) for n = 0..1000</a>
%F A239077 G.f.: -(x^22 +2*x^17 -10*x^12 -2*x^11 +2*x^10 -2*x^9 -2*x^8 +6*x^7 +4*x^6 -2*x^5 +2*x^4 +2*x^3 +2*x^2-1) / (x^32 +x^31 +x^30 -x^29 -x^28 +7*x^27 +5*x^26 +x^25 -5*x^24 -3*x^23 -x^22 -8*x^21 -16*x^20 +8*x^18 -40*x^17 -36*x^16 +20*x^14 +12*x^13 +64*x^12 +52*x^11 +19*x^10 -5*x^9 -13*x^8 -27*x^7 -19*x^6 +x^5 -x^4 -x^3 -3*x^2 -x+1).
%p A239077 gf:= -(x^22 +2*x^17 -10*x^12 -2*x^11 +2*x^10 -2*x^9 -2*x^8 +6*x^7 +4*x^6 -2*x^5 +2*x^4 +2*x^3 +2*x^2-1) / (x^32 +x^31 +x^30 -x^29 -x^28 +7*x^27 +5*x^26 +x^25 -5*x^24 -3*x^23 -x^22 -8*x^21 -16*x^20 +8*x^18 -40*x^17 -36*x^16 +20*x^14 +12*x^13 +64*x^12 +52*x^11 +19*x^10 -5*x^9 -13*x^8 -27*x^7 -19*x^6 +x^5 -x^4 -x^3 -3*x^2 -x+1):
%p A239077 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A239077 seq(a(n), n=0..40);
%t A239077 CoefficientList[Series[-(x^22 + 2 x^17 - 10 x^12 - 2 x^11 + 2 x^10 - 2 x^9 - 2 x^8 + 6 x^7 + 4 x^6 - 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 - 1)/(x^32 + x^31 + x^30 - x^29 - x^28 + 7 x^27 + 5 x^26 + x^25 - 5 x^24 - 3 x^23 - x^22 - 8 x^21 - 16 x^20 + 8 x^18 - 40 x^17 - 36 x^16 + 20 x^14 + 12 x^13 + 64 x^12 + 52 x^11 + 19 x^10 - 5 x^9 - 13 x^8 - 27 x^7 - 19 x^6 + x^5 - x^4 - x^3 - 3 x^2 - x + 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Mar 12 2014 *)
%Y A239077 Cf. A000085, A238888.
%K A239077 nonn,easy
%O A239077 0,3
%A A239077 _Joerg Arndt_ and _Alois P. Heinz_, Mar 10 2014