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

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

Offset

1,3

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A163402 A288757 A289900 * A082707 A087193 A348141

Adjacent sequences: A235059 A235060 A235061 * A235063 A235064 A235065

Keyword

nonn,nice

Author

Ralf Stephan, Jan 03 2014

Status

approved