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

%I A197880 #21 May 10 2019 23:59:30
%S A197880 1,6,30,35,70,77,3003,1430,24310,230945,969969,4056234,676039,312018,
%T A197880 1292646,33393355,2203961430,90751353,3357800061,1531628098,
%U A197880 156991880045,5786272150230,105204948186,107492012277,35830670759,3654728417418,14900046624858
%N A197880 Squarefree part of ((2n-1)!)^(2n-3).
%C A197880 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 A197880 a(n) = A007913(A134367(2*n-1)). - _R. J. Mathar_, Oct 25 2011
%p A197880 A134367 := proc(n)
%p A197880         (n!)^(n-2) ;
%p A197880 end proc:
%p A197880 A007913 := proc(n)
%p A197880         a := 1 ;
%p A197880         for pf in ifactors(n)[2] do
%p A197880                 p := op(1,pf) ;
%p A197880                 e := op(2,pf) ;
%p A197880                 a := a*p^(e mod 2) ;
%p A197880         end do:
%p A197880         a ;
%p A197880 end proc:
%p A197880 A198480 := proc(n)
%p A197880         A007913( A134367(2*n-1)) ;
%p A197880 end proc:
%p A197880 seq(A198480(n),n=1..10) ; # _R. J. Mathar_, Oct 25 2011
%t A197880 aa = {}; data = Table[kk = Sqrt[(n!)^(n - 2)], {n, 1, 100, 2}]; sp = data /. Sqrt[_] -> 1; sfp = data/sp; sfp^2
%Y A197880 Cf. A007913, A134367, A198481.
%K A197880 nonn
%O A197880 1,2
%A A197880 _Artur Jasinski_, Oct 25 2011