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 A051695 Number of degree-n even permutations of order exactly 4. 17
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 FORMULA 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A001473, A048099, A051685. Sequence in context: A295982 A065949 A224541 * A304165 A232588 A097372 Adjacent sequences:  A051692 A051693 A051694 * A051696 A051697 A051698 KEYWORD easy,nonn AUTHOR EXTENSIONS Terms a(19) and beyond from Andrew Howroyd, Feb 01 2020 STATUS approved

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Last modified July 3 01:56 EDT 2022. Contains 355029 sequences. (Running on oeis4.)