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

0,2

Links

Table of n, a(n) for n=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

Maple

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

Prog

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

Crossrefs

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

Cf. A056982.

Sequence in context: A203281 A255576 A065404 * A330824 A189806 A222748

Adjacent sequences: A327493 A327494 A327495 * A327497 A327498 A327499

Keyword

nonn,easy

Author

Peter Luschny, Sep 29 2019

Status

approved