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A285862
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Number of permutations of [2n] with n ordered cycles such that equal-sized cycles are ordered with increasing least elements.
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4
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1, 1, 19, 1005, 62601, 6061545, 868380535, 142349568361, 27564092244689, 6325532235438273, 1673378033771898675, 505141951803309946125, 170002056228253072537065, 63255335047795174479833625, 25805276337820748477042392695, 11427131417576257617280878155625
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 1: (12).
a(2) = 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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b:= proc(n, i, p) option remember; expand(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
[multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)))
end:
a:= n-> coeff(b(2*n$2, 0), x, n):
seq(a(n), n=0..20);
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MATHEMATICA
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multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Expand[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[b[n - i*j, i - 1, p + j]*(i - 1)!^j*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2*x^j, {j, 0, n/i}]]];
a[n_] := Coefficient[b[2n, 2n, 0], x, n];
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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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