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%I #10 Mar 09 2014 18:37:27
%S 0,0,0,0,0,0,10,48,170,515,1471,4119,11605,32568,90756,250432,684816,
%T 1858440,5016359,13484339,36124302,96487740,257021991,682958487,
%U 1810749368,4791502490,12657090174,33383355375,87928909275,231312358250,607831534982,1595624166626
%N Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 5.
%H Joerg Arndt and Alois P. Heinz, <a href="/A238916/b238916.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: see Maple program.
%e a(6) = 10: 623451, 623541, 624351, 625431, 632451, 632541, 643251, 645231, 653421, 654321.
%e a(7) = 48: 1734562, 1734652, 1735462, ..., 6735412, 6743512, 6754312.
%e a(8) = 170: 12845673, 12845763, 12846573, ..., 67583124, 67845123, 67854123.
%p gf:= (x^34 +x^33 +x^32 -x^30 +7*x^29 +4*x^28 +5*x^27 +3*x^26 -7*x^25 +2*x^24 +2*x^22 -4*x^21 -14*x^20 -38*x^19 -8*x^18 -14*x^17 -52*x^16 +12*x^15 +26*x^14 -56*x^13 -53*x^12 +79*x^11 +79*x^10 +42*x^9 +55*x^8 +49*x^7 -26*x^6 -65*x^5 -35*x^4 +13*x^3 +34*x^2 +28*x +10)*x^6 / ((x^16 +x^15 +2*x^14 +x^13 +x^12 +2*x^11 +x^10 +3*x^9 -4*x^8 -5*x^7 -9*x^6 -6*x^5 -x^4 -x^3 -2*x^2 -x +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 a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..40);
%t CoefficientList[Series[(x^34 + x^33 + x^32 - x^30 + 7 x^29 + 4 x^28 + 5 x^27 + 3 x^26 - 7 x^25 + 2 x^24 + 2 x^22 - 4 x^21 - 14 x^20 - 38 x^19 - 8 x^18 - 14 x^17 - 52 x^16 + 12 x^15 + 26 x^14 - 56 x^13 - 53 x^12 + 79 x^11 + 79 x^10 + 42 x^9 + 55 x^8 + 49 x^7 - 26 x^6 - 65 x^5 - 35 x^4 + 13 x^3 + 34 x^2 + 28 x + 10) x^6/((x^16 + x^15 + 2 x^14 + x^13 + x^12 + 2 x^11 + x^10 + 3 x^9 - 4 x^8 - 5 x^7 - 9 x^6 - 6 x^5 - x^4 - x^3 - 2 x^2 - x + 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, 40}], x] (* _Vincenzo Librandi_, Mar 09 2014 *)
%Y Column k=5 of A238889.
%K nonn
%O 0,7
%A _Joerg Arndt_ and _Alois P. Heinz_, Mar 07 2014
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