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A365229
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Sum over all k of 1/k! times the number of permutations of [n] for which the difference between the longest and the shortest cycle length is k.
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2
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1, 1, 2, 6, 20, 85, 382, 2219, 13624, 100293, 811914, 7594015, 74507490, 862987151, 10327793088, 139175089681, 1966790900028, 30983071424315, 496696984054286, 8925920862110603, 162253809011669330, 3228438870635420315, 65677024568975412036, 1448358661756969370985
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OFFSET
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0,3
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COMMENTS
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a(0) = 1 by convention.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..max(0,n-2)} A364967(n,k)/k!.
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MAPLE
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b:= proc(n, l, m) option remember; `if`(n=0, 1/(m-l)!, add((j-1)!
*b(n-j, min(l, j), max(m, j))*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n$2, 0):
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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