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A238913
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Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 2.
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2
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0, 0, 0, 1, 3, 7, 16, 35, 74, 153, 312, 629, 1257, 2495, 4926, 9684, 18972, 37064, 72243, 140547, 273007, 529626, 1026369, 1987260, 3844919, 7434542, 14368115, 27756229, 53600223, 103476920, 199715716, 385381128, 743520256, 1434272329, 2766414007, 5335290607
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OFFSET
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0,5
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LINKS
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Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: x^3*(x+1)/((x^2+x-1)*(x^4+x^3+x^2+x-1)).
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EXAMPLE
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a(3) = 1: 321.
a(4) = 3: 1432, 3214, 3412.
a(5) = 7: 12543, 14325, 14523, 21543, 32145, 32154, 34125.
a(6) = 16: 123654, 125436, 125634, 132654, 143256, 143265, 145236, 213654, 215436, 215634, 321456, 321465, 321546, 321654, 341256, 341265.
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MAPLE
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gf:= x^3*(1+x)/((x^2+x-1)*(x^4+x^3+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^3 (x + 1)/((x^2 + x - 1) (x^4 + x^3 + x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 09 2014 *)
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CROSSREFS
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Column k=2 of A238889.
Sequence in context: A240740 A239257 A268394 * A133124 A104004 A101509
Adjacent sequences: A238910 A238911 A238912 * A238914 A238915 A238916
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KEYWORD
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nonn
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AUTHOR
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Joerg Arndt and Alois P. Heinz, Mar 07 2014
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STATUS
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approved
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