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A238915
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Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 4.
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2
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0, 0, 0, 0, 0, 4, 18, 55, 151, 399, 1061, 2792, 7252, 18572, 47051, 118291, 295718, 735776, 1823183, 4501151, 11077398, 27187053, 66567357, 162655518, 396728446, 966109074, 2349342360, 5705883591, 13842565488, 33549053111, 81238182806, 196560818348
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OFFSET
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0,6
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (3, 0, -3, 1, 2, -7, -16, -7, -21, -12, -9, 1, 16, 7, 11, 0, 3, 2, 1, 1, -2, -1, -1).
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FORMULA
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G.f.: (x^12 -x^9 -x^8 +2*x^7 -x^6 +3*x^5 -4*x^4 -2*x^3 +x^2 +6*x +4)*x^5 / ((x+1)*(x^6 -x^5 +x^4 -3*x^3 +3*x^2 -3*x+1) *(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)).
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EXAMPLE
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a(5) = 4: 52341, 52431, 53241, 54321.
a(6) = 18: 163452, 163542, 164352, 165432, 361452, 361542, 463152, 465132, 523416, 523614, 524316, 526413, 532416, 532614, 543216, 546213, 563412, 564312.
a(7) = 55: 1274563, 1274653, 1275463, ..., 5637124, 5643127, 5674123.
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MAPLE
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gf:= (x^12 -x^9 -x^8 +2*x^7 -x^6 +3*x^5 -4*x^4 -2*x^3 +x^2 +6*x +4)*x^5 /
((x+1)*(x^6 -x^5 +x^4 -3*x^3 +3*x^2 -3*x+1) *(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)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);
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MATHEMATICA
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CoefficientList[Series[(x^12 - x^9 - x^8 + 2 x^7 - x^6 + 3 x^5 - 4 x^4 - 2 x^3 + x^2 + 6 x + 4) x^5/((x + 1) (x^6 - x^5 + x^4 - 3 x^3 + 3 x^2 - 3 x + 1) (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, 0, 40}], x] (* Vincenzo Librandi, Mar 09 2014 *)
LinearRecurrence[{3, 0, -3, 1, 2, -7, -16, -7, -21, -12, -9, 1, 16, 7, 11, 0, 3, 2, 1, 1, -2, -1, -1}, {0, 0, 0, 0, 0, 4, 18, 55, 151, 399, 1061, 2792, 7252, 18572, 47051, 118291, 295718, 735776, 1823183, 4501151, 11077398, 27187053, 66567357}, 40] (* Harvey P. Dale, Mar 09 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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