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A198481 Square root of the largest square dividing ((2n-1)!)^(2n-3).

%I A198481 #13 May 24 2024 18:59:59
%S A198481 1,1,240,304819200,3440500260470784000,
%T A198481 1827912356210202139164672000000000,
%U A198481 13482302715547740229948201750717130814259200000000000
%N A198481 Square root of the largest square dividing ((2n-1)!)^(2n-3).
%C A198481 For the complementary squarefree parts see A197880.
%F A198481 a(n) = A000188(A134367(2*n-1)). - _R. J. Mathar_, Oct 25 2011
%p A198481 A000188 := proc(n)
%p A198481         a := 1 ;
%p A198481         for pf in ifactors(n)[2] do
%p A198481                 p := op(1,pf) ;
%p A198481                 e := op(2,pf) ;
%p A198481                 a := a*p^(floor(e/2)) ;
%p A198481         end do:
%p A198481         a ;
%p A198481 end proc:
%p A198481 A198481 := proc(n)
%p A198481         A000188( A134367(2*n-1)) ;
%p A198481 end proc:
%p A198481 seq(A198481(n),n=1..10) ; # _R. J. Mathar_, Oct 25 2011
%t A198481 aa = {}; data = Table[kk = Sqrt[(n!)^(n - 2)], {n, 1, 100, 2}]; sp = data /. Sqrt[_] -> 1; sfp = data/sp; sp
%t A198481 Sqrt[#]&/@Table[Max[Select[Divisors[((2n-1)!)^(2n-3)],IntegerQ[Sqrt[#]]&]],{n,7}] (* _Harvey P. Dale_, May 24 2024 *)
%Y A198481 Cf. A134367, A197880.
%K A198481 nonn
%O A198481 1,3
%A A198481 _Artur Jasinski_, Oct 25 2011