A197880 - OEIS

%I #21 May 10 2019 23:59:30

%S 1,6,30,35,70,77,3003,1430,24310,230945,969969,4056234,676039,312018,

%T 1292646,33393355,2203961430,90751353,3357800061,1531628098,

%U 156991880045,5786272150230,105204948186,107492012277,35830670759,3654728417418,14900046624858

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

%C 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.

%F a(n) = A007913(A134367(2*n-1)). - _R. J. Mathar_, Oct 25 2011

%p A134367 := proc(n)

%p         (n!)^(n-2) ;

%p end proc:

%p A007913 := proc(n)

%p         a := 1 ;

%p         for pf in ifactors(n)[2] do

%p                 p := op(1,pf) ;

%p                 e := op(2,pf) ;

%p                 a := a*p^(e mod 2) ;

%p         end do:

%p         a ;

%p end proc:

%p A198480 := proc(n)

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

%p end proc:

%p seq(A198480(n),n=1..10) ; # _R. J. Mathar_, Oct 25 2011

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

%Y Cf. A007913, A134367, A198481.

%K nonn

%O 1,2

%A _Artur Jasinski_, Oct 25 2011