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A368678
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Number of permutations of [n] whose cycle maxima sum to 2n.
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5
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1, 0, 0, 1, 2, 10, 41, 260, 1552, 12818, 101280, 1021908, 10154064, 121656672, 1447205472, 20215013184, 280271024640, 4457067906240, 70826580095040, 1264147627392000, 22588177271650560, 448332829478760960, 8899910723677639680, 194096853444946636800
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OFFSET
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0,5
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LINKS
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FORMULA
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EXAMPLE
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a(0) = 1: the empty permutation.
a(3) = 1: (1)(2)(3).
a(4) = 2: (1)(23)(4), (1)(24)(3).
a(5) = 10: (12)(3)(45), (13)(2)(45), (1)(234)(5), (1)(243)(5), (1)(235)(4),
(1)(253)(4), (145)(2)(3), (154)(2)(3), (1)(24)(35), (1)(25)(34).
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MAPLE
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b:= proc(n) option remember;
`if`(n=0, 1, expand(b(n-1)*(t-n+x^n)))
end:
a:= n-> coeff(subs(t=n, b(n)), x, 2*n):
seq(a(n), n=0..23);
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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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