A134367 -id:A134367 - cp's OEIS frontend

A197880 Squarefree part of ((2n-1)!)^(2n-3).

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

Offset: 1

Artur Jasinski, Oct 25 2011

nonn

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.

Cf. A007913, A134367, A198481.

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

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

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

A127488 a(n) = (n^2)!/(2*(n!)).

Original entry on oeis.org

6, 30240, 435891456000, 64630041847212441600000, 258328699159653623241666283438080000000

Offset: 2

Artur Jasinski, Jan 16 2007

nonn

Cf. A000142, A001044, A000442, A036740, A010050, A009445, A134366, A134367, A134368, A134369, A134371, A134372, A134373, A134374, A134374

Mathematica
```
Table[(n^2)!/(2(n!)), {n, 2, 6}]
```

a(n) ~ n^(2*n^2 - n + 1/2) / (2 * exp(n*(n-1))). - Vaclav Kotesovec, Oct 26 2017

cp's OEIS Frontend

A197880 Squarefree part of ((2n-1)!)^(2n-3).

Views

Author

Keywords

Comments

Crossrefs

Programs

Maple

Mathematica

Formula