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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.

%I A327496 #11 May 31 2022 22:26:46
%S A327496 1,16,64,1024,16384,262144,1048576,16777216,1073741824,17179869184,
%T A327496 68719476736,1099511627776,17592186044416,281474976710656,
%U A327496 1125899906842624,18014398509481984,4611686018427387904,73786976294838206464,295147905179352825856,4722366482869645213696
%N 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.
%F A327496 a(n) = denominator(r(n)) where r(n) = Sum_{j=0..n} j!^2 / (2^j*floor(j/2))^4.
%F A327496 a(n) = 4^A327492(n). - _Kevin Ryde_, May 31 2022
%p A327496 A327496 := n -> denom(add(j!^2 / (2^j*iquo(j, 2)!)^4, j=0..n)):
%p A327496 seq(A327496(n), n=0..19);
%o A327496 (SageMath)
%o A327496 @cached_function
%o A327496 def A327496(n):
%o A327496     if n == 0: return 1
%o A327496     r = valuation(n, 2) if 4.divides(n) else n % 2 + 1
%o A327496     return 4^r * A327496(n-1)
%o A327496 print([A327496(n) for n in (0..19)])
%o A327496 (PARI) a(n) = 1 << (4*n - 2*hammingweight(n>>1)); \\ _Kevin Ryde_, May 31 2022
%Y A327496 Cf. A327491, A327492, A327493, A327494, A327495.
%Y A327496 Cf. A056982.
%K A327496 nonn,easy
%O A327496 0,2
%A A327496 _Peter Luschny_, Sep 29 2019