A187791 Repeat n+1 times 2^A005187(n).

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

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.

OEIS Wiki, Autosequence

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 2013 *)
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: A260825 A330763 A138102 * A372260 A245235 A151924

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