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A235062 Odd part of n-th superfactorial (A000178).

%I A235062 #17 Jul 09 2022 11:10:41
%S A235062 1,1,3,9,135,6075,1913625,602791875,1708914965625,24223869637734375,
%T A235062 3777106873263732421875,1766836167640942433642578125,
%U A235062 10744263248137144009663040771484375,457356694421659081059931729616180419921875
%N A235062 Odd part of n-th superfactorial (A000178).
%C A235062 Partial products of A049606(n). Denominator of 2^(2n)/A000178(n).
%H A235062 Ralf Stephan, <a href="/A235062/b235062.txt">Table of n, a(n) for n = 1..100</a>
%F A235062 a(n) = A000265(A000178(n)) = A000178(n)/2^A174605(n) = A000178(n)/2^A007814(A000178(n)).
%e A235062 6!5!4!3!2!1! = 24883200 = 2^12 * 6075, so a(6) = 6075.
%t A235062 #/2^IntegerExponent[#,2]&/@Rest[FoldList[Times,1,Range[15]!]] (* _Harvey P. Dale_, Mar 04 2014 *)
%o A235062 (PARI) a(n)=p=prod(k=1,n,k!);p/2^valuation(p,2)
%o A235062 (Python)
%o A235062 from math import prod
%o A235062 from operator import mul
%o A235062 from itertools import accumulate
%o A235062 def A235062(n): return prod(map(lambda n:n>>(~n&n-1).bit_length(),accumulate(range(1,n+1),mul))) # _Chai Wah Wu_, Jul 08 2022
%Y A235062 Cf. A000178, A000265, A007814, A049606, A174605.
%K A235062 nonn,nice
%O A235062 1,3
%A A235062 _Ralf Stephan_, Jan 03 2014