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A197880
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Squarefree part of ((2n-1)!)^(2n-3).
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1
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1, 6, 30, 35, 70, 77, 3003, 1430, 24310, 230945, 969969, 4056234, 676039, 312018, 1292646, 33393355, 2203961430, 90751353, 3357800061, 1531628098, 156991880045, 5786272150230, 105204948186, 107492012277, 35830670759, 3654728417418, 14900046624858
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OFFSET
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1,2
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COMMENTS
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These numbers are quadratic fields of extensions of polynomials of odd degree obtained by taken 2n-1 terms of expansion of e^x in power series at 0. All these polynomials have Galois group S(2n-1) over rationals.
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LINKS
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FORMULA
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MAPLE
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(n!)^(n-2) ;
end proc:
a := 1 ;
for pf in ifactors(n)[2] do
p := op(1, pf) ;
e := op(2, pf) ;
a := a*p^(e mod 2) ;
end do:
a ;
end proc:
end proc:
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MATHEMATICA
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aa = {}; data = Table[kk = Sqrt[(n!)^(n - 2)], {n, 1, 100, 2}]; sp = data /. Sqrt[_] -> 1; sfp = data/sp; sfp^2
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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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