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A285853
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Number of permutations of [n] with two ordered cycles such that equal-sized cycles are ordered with increasing least elements.
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3
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1, 6, 19, 100, 508, 3528, 24876, 219168, 1980576, 21257280, 234434880, 2972885760, 38715943680, 566931294720, 8514866707200, 141468564787200, 2407290355814400, 44753976117043200, 850965783594393600, 17505896073523200000, 367844990453821440000
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OFFSET
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2,2
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LINKS
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EXAMPLE
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a(2) = 1: (1)(2).
a(3) = 6: (1)(23), (23)(1), (2)(13), (13)(2), (3)(12), (12)(3).
a(4) = 19: (123)(4), (4)(123), (132)(4), (4)(132), (124)(3), (3)(124), (142)(3), (3)(142), (134)(2), (2)(134), (143)(2), (2)(143), (1)(234), (234)(1), (1)(243), (243)(1), (12)(34), (13)(24), (14)(23).
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MAPLE
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a:= n-> 2*add(binomial(n, k)*(k-1)!*(n-k-1)!, k=1..n/2)-
`if`(n::even, 3/2*binomial(n, n/2)*(n/2-1)!^2, 0):
seq(a(n), n=2..25);
# second Maple program:
a:= proc(n) option remember; `if`(n<5, [0, 1, 6, 19][n],
((2*n-1)*(n-1)*a(n-1)+(n-2)*(2*n^2-5*n-1)*a(n-2)
-(n-3)^2*((2*n^2-5*n+4)*a(n-3)+(n-4)^2*a(n-4)))/(2*n))
end:
seq(a(n), n=2..25);
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MATHEMATICA
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Table[(n-1)!*(2*HarmonicNumber[n] - (3 + (-1)^n)/n), {n, 2, 25}] (* Vaclav Kotesovec, Apr 29 2017 *)
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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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