A198481 -id:A198481

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A197880

Squarefree part of ((2n-1)!)^(2n-3).

+10
1

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

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..27.

FORMULA

a(n) = A007913(A134367(2*n-1)). - R. J. Mathar, Oct 25 2011

MAPLE

A134367 := proc(n)

(n!)^(n-2) ;

end proc:

A007913 := proc(n)

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:

A198480 := proc(n)

A007913( A134367(2*n-1)) ;

end proc:

seq(A198480(n), n=1..10) ; # R. J. Mathar, Oct 25 2011

MATHEMATICA

aa = {}; data = Table[kk = Sqrt[(n!)^(n - 2)], {n, 1, 100, 2}]; sp = data /. Sqrt[_] -> 1; sfp = data/sp; sfp^2

CROSSREFS

Cf. A007913, A134367, A198481.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 25 2011

STATUS

approved

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