|
Search: id:A164658
|
|
|
| A164658 |
|
Numerators of coefficients of integrated Chebyshev polynomials T(n,x) (in increasing order of powers of x). |
|
+0
6
|
|
| 1, 0, 1, -1, 0, 2, 0, -3, 0, 1, 1, 0, -8, 0, 8, 0, 5, 0, -5, 0, 8, -1, 0, 6, 0, -48, 0, 32, 0, -7, 0, 14, 0, -56, 0, 8, 1, 0, -32, 0, 32, 0, -256, 0, 128, 0, 9, 0, -30, 0, 72, 0, -72, 0, 128, -1, 0, 50, 0, -80, 0, 160, 0, -1280, 0, 512, 0, -11, 0, 55, 0, -616, 0, 352, 0, -1408, 0, 256, 1, 0, -24, 0, 168, 0, -512, 0, 768
(list; table; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
The denominators are given in A164659.
The column nr. m of the rational triangle A164658/A164659 when multiplied by m/2^(m-2) becomes (with shifted offset) the column nr. m-1 divided by 2^(m-1) of the Chebyshev T-triangle A053120 for m=1,2,3,...
|
|
LINKS
|
W. Lang: First eleven rows of the rational coefficients.
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
a(n,m) = numerator(b(n,m)), with int(T(n,x))= sum(b(n,m)*x^m,m=1..n+1), n>=0, where T(n,x) are Chebyshevs polynomials of the first kind.
|
|
EXAMPLE
|
Rationals a(n,m)/A164659(n,m) = [1], [0, 1/2], [-1, 0, 2/3], [0, -3/2, 0, 1], [1, 0, -8/3, 0, 8/5],...
|
|
CROSSREFS
|
Row sums of triangle give A164662.
A053120: coefficients of T-polynomials.
Row sums of rational triangle A164658/A164659 are given by A164660/A164661.
Sequence in context: A078442 A135523 A135685 this_sequence A079067 A160271 A065134
Adjacent sequences: A164655 A164656 A164657 this_sequence A164659 A164660 A164661
|
|
KEYWORD
|
sign,frac,tabl,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang@physik.uni-karlsruhe.de) Oct 16 2009
|
|
|
Search completed in 0.002 seconds
|
