A231234 Denominators related to A206771 and Lorentz gamma factor.

1, 1, 1, 8, 4, 128, 128, 1024, 256, 32768, 32768, 262144, 131072, 4194304, 4194304, 33554432, 4194304, 2147483648, 2147483648, 17179869184, 8589934592, 274877906944, 274877906944, 2199023255552, 549755813888, 70368744177664

Offset: 0

Author

Jean-François Alcover and Paul Curtz, Nov 06 2013

Keywords

• nonn
• frac

Comments

See A206771.

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).

Crossrefs

Cf. A001803, A001790, A006519, A046161, A206771.

Programs

Mathematica

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}]
(* 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}]

Formula

a(n) = denominator(4^(1-n)*binomial(2*n-2, n-1))/2^valuation(n, 2) (where valuation(n,2) = A007814(n)).

a(n) = 2^(2*n-2-adic valuation(n, 2)-valuation(binomial(2*n-2, n-1), 2)).

a(n) = A046161(n-1)/A006519(n).