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A231234 Denominators related to A206771 and Lorentz gamma factor. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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).

LINKS

Table of n, a(n) for n=0..25.

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).

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}]

CROSSREFS

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

Sequence in context: A112589 A038282 A268482 * A096687 A326955 A199374

Adjacent sequences:  A231231 A231232 A231233 * A231235 A231236 A231237

KEYWORD

nonn,frac

AUTHOR

Jean-Fran├žois Alcover and Paul Curtz, Nov 06 2013

STATUS

approved

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Last modified January 17 15:20 EST 2022. Contains 350402 sequences. (Running on oeis4.)