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A187791 Repeat n+1 times 2^A005187(n). 2
1, 2, 2, 8, 8, 8, 16, 16, 16, 16, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256, 256, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 32768, 32768, 32768, 32768, 32768, 32768, 32768, 32768, 32768, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536, 65536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the denominators of the antidiagonals of the Lorentz factor, which can be written A001790(n)/A046161(n), and its differences.

1,           1/2,     3/8,      5/16,    35/128,     63/256,...  the Lorentz gamma factor,

-1/2,       -1/8,   -1/16,    -5/128,    -7/256,   -21/1024, ...  -A098597(n)/A046161(n+1),from the Lorentz (beta) factor,

3/8,        1/16,   3/128,     3/256,    7/1024,     9/2048,...  A161200(n+2)/A046161(n+2),

-5/16,    -5/128,  -3/256,   -5/1024,   -5/2048,  -45/32768,...  A161202(n+3)/A046161(n+4),

35/128,    7/256,  7/1024,    5/2048,  35/32768,   35/65536, ...

-63/256, -21/1024, -9/2048, -45/32768, -35/65536, -63/262144, ...  .

Like 1/n and A164555(n)/A027642(n), the Lorentz factor is an autosequence of the second kind. The first column is the signed sequence.

The main diagonal is (-1)^n *A001790(n)/A061549(n).

The Lorentz factor is the differences of (0, followed by A001803(n)) / (1, followed by A046161(n)).

PiSK(n-2)=(0, 0, followed by A001803(n)) / (1, 1, followed by A046161(n)) is also an autosequence of second kind.

Remember that an autosequence of the second kind is a sequence whose inverse binomial transform is the sequence signed, with its main diagonal being the double of its first upper diagonal. - Paul Curtz, Oct 13 2013

LINKS

Table of n, a(n) for n=0..54.

Wikipedia, Lorentz Factor.

FORMULA

Repeat A046161(n) n+1 times. Triangle.

EXAMPLE

1,

2,   2,

8,   8,  8,

16, 16, 16, 16.

MATHEMATICA

Flatten[Table[Denominator[Binomial[2n, n]/4^n], {n, 0, 19}, {n + 1}]] (* Alonso del Arte, Jan 07 2013 *)

(* Checking with the antidiagonals *) diff = Table[ Differences[ CoefficientList[ Series[1/Sqrt[1 - x], {x, 0, 9}], x], n], {n, 0, 9}]; Table[ diff[[n-k+1, k]] // Denominator, {n, 0, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jan 07 2113 *)

Flatten[Table[2^IntegerExponent[(2*n)!, 2], {n, 0, 19}, {n + 1}]]; (* Jean-François Alcover, Mar 27 2013, after A005187 *)

CROSSREFS

Cf. A003506.

Sequence in context: A196066 A260825 A138102 * A245235 A151924 A268342

Adjacent sequences:  A187788 A187789 A187790 * A187792 A187793 A187794

KEYWORD

nonn,frac,less

AUTHOR

Paul Curtz, Jan 06 2013

EXTENSIONS

New definition by M. F. Hasler

STATUS

approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)