A327496 a(n) = a(n - 1) * 4^r where r = valuation(n, 2) if 4 divides n else r = (n mod 2) + 1; a(0) = 1. The denominators of A327495.

1, 16, 64, 1024, 16384, 262144, 1048576, 16777216, 1073741824, 17179869184, 68719476736, 1099511627776, 17592186044416, 281474976710656, 1125899906842624, 18014398509481984, 4611686018427387904, 73786976294838206464, 295147905179352825856, 4722366482869645213696

Offset: 0

Author

Peter Luschny, Sep 29 2019

Keywords

• nonn
• easy

Crossrefs

Cf. A327491, A327492, A327493, A327494, A327495.

Cf. A056982.

Programs

Maple

A327496 := n -> denom(add(j!^2 / (2^j*iquo(j, 2)!)^4, j=0..n)):
seq(A327496(n), n=0..19);

PARI

a(n) = 1 << (4*n - 2*hammingweight(n>>1)); \\ Kevin Ryde, May 31 2022

SageMath

@cached_function
def A327496(n):
    if n == 0: return 1
    r = valuation(n, 2) if 4.divides(n) else n % 2 + 1
    return 4^r * A327496(n-1)
print([A327496(n) for n in (0..19)])

Formula

a(n) = denominator(r(n)) where r(n) = Sum_{j=0..n} j!^2 / (2^j*floor(j/2))^4.

a(n) = 4^A327492(n). - Kevin Ryde, May 31 2022