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A051695
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Number of degree-n even permutations of order exactly 4.
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17
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0, 0, 0, 0, 0, 90, 630, 3780, 18900, 94500, 457380, 3825360, 31505760, 312432120, 2704501800, 22984481520, 179863997040, 1531709328240, 13078616488560, 147223414987200, 1657733805020160, 20131890668255520, 226464779237447520, 2542924546378413120, 27053572399079688000
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OFFSET
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1,6
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..200
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FORMULA
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a(n) = (A001473(n) + A051685(n))/2.
E.g.f.: (exp(x + x^2/2 + x^4/4) + exp(x - x^2/2 - x^4/4) - exp(x + x^2/2) - exp(x - x^2/2))/2. - Andrew Howroyd, Feb 01 2020
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MATHEMATICA
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m = 26; ((Exp[x + x^2/2 + x^4/4] + Exp[x - x^2/2 - x^4/4] - Exp[x + x^2/2] - Exp[x - x^2/2])/2 + O[x]^m // CoefficientList[#, x]& // Rest) * Range[m - 1]! (* Jean-François Alcover, Feb 09 2020, after Andrew Howroyd *)
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PROG
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(PARI) seq(n)={my(A=O(x*x^n)); Vec(serlaplace(exp(x + x^2/2 + x^4/4 + A) + exp(x - x^2/2 - x^4/4 + A) - exp(x + x^2/2 + A) - exp(x - x^2/2 + A))/2, -n)} \\ Andrew Howroyd, Feb 01 2020
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CROSSREFS
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Cf. A001473, A048099, A051685.
Sequence in context: A295982 A065949 A224541 * A304165 A232588 A097372
Adjacent sequences: A051692 A051693 A051694 * A051696 A051697 A051698
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic
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EXTENSIONS
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Terms a(19) and beyond from Andrew Howroyd, Feb 01 2020
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STATUS
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approved
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