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%I #12 Sep 07 2014 08:17:18
%S 1,1,1,8,4,128,128,1024,256,32768,32768,262144,131072,4194304,4194304,
%T 33554432,4194304,2147483648,2147483648,17179869184,8589934592,
%U 274877906944,274877906944,2199023255552,549755813888,70368744177664
%N Denominators related to A206771 and Lorentz gamma factor.
%C See A206771.
%C In addition, it can be noticed that a(n) is always a power of 2 and that a(2n-1)/a(2n) is A006519(n).
%F a(n) = denominator(4^(1-n)*binomial(2*n-2, n-1))/2^valuation(n, 2) (where valuation(n,2) = A007814(n)).
%F a(n) = 2^(2*n-2-adic valuation(n, 2)-valuation(binomial(2*n-2, n-1), 2)).
%F a(n) = A046161(n-1)/A006519(n).
%t max = 25; A001803 = CoefficientList[Series[(1 - x)^(-3/2), {x, 0, max}], x] // Numerator; A001790 = CoefficientList[Series[1/Sqrt[(1 - x)], {x, 0, max}], x] // Numerator; A046161 = Table[Binomial[2 n, n]/4^n, {n, 0, max}] // Denominator; a[0] = 1; a[n_] := (A001803[[n]] + A001790[[n]])/(2*A046161[[n]]) // Denominator; Table[a[n], {n, 0, max}]
%t (* or, directly: *) a[0] = 1; a[n_] := Denominator[4^(1-n)*Binomial[2*n-2, n-1]]/2^IntegerExponent[n, 2]; Table[a[n], {n, 0, max}]
%Y Cf. A001803, A001790, A006519, A046161, A206771.
%K nonn,frac
%O 0,4
%A _Jean-François Alcover_ and _Paul Curtz_, Nov 06 2013
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