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

1, 1, 3, 9, 135, 6075, 1913625, 602791875, 1708914965625, 24223869637734375, 3777106873263732421875, 1766836167640942433642578125, 10744263248137144009663040771484375, 457356694421659081059931729616180419921875

Offset: 1

Author

Ralf Stephan, Jan 03 2014

Keywords

• nonn
• nice

Comments

Partial products of A049606(n). Denominator of 2^(2n)/A000178(n).

Examples

			6!5!4!3!2!1! = 24883200 = 2^12 * 6075, so a(6) = 6075.
		

Links

• Ralf Stephan, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000178, A000265, A007814, A049606, A174605.

Programs

Mathematica

#/2^IntegerExponent[#,2]&/@Rest[FoldList[Times,1,Range[15]!]] (* Harvey P. Dale, Mar 04 2014 *)

PARI

a(n)=p=prod(k=1,n,k!);p/2^valuation(p,2)

Python

from math import prod
from operator import mul
from itertools import accumulate
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

Formula

a(n) = A000265(A000178(n)) = A000178(n)/2^A174605(n) = A000178(n)/2^A007814(A000178(n)).