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A048099
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Number of degree-n even permutations of order exactly 2.
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18
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0, 0, 0, 3, 15, 45, 105, 315, 1323, 5355, 18315, 63855, 272415, 1264263, 5409495, 22302735, 101343375, 507711375, 2495918223, 11798364735, 58074029055, 309240315615, 1670570920095, 8792390355903, 46886941456575, 264381946998975, 1533013006902975, 8785301059346175, 50439885753378303
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OFFSET
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1,4
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LINKS
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FORMULA
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E.g.f.: (exp(x + x^2/2) + exp(x - x^2/2))/2 - exp(x). - Andrew Howroyd, Feb 01 2020
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MATHEMATICA
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PROG
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(PARI) a(n) = sum(i=1, n\4, binomial(n, 4*i)*(4*i)!/(2^(2*i)*(2*i)!)); \\ Michel Marcus, May 17 2018
(PARI) seq(n)={my(A=O(x*x^n)); Vec(serlaplace(exp(x + x^2/2 + A) + exp(x - x^2/2 + A) - 2*exp(x + A))/2, -n)} \\ Andrew Howroyd, Feb 01 2020
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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