|
Search: id:A008314
|
|
|
| A008314 |
|
Triangle of expansions of one half of powers of 2*x in terms of Chebyshev polynomials T_n (x). |
|
+0
3
|
|
| 1, 1, 1, 1, 1, 3, 1, 4, 3, 1, 5, 10, 1, 6, 15, 10, 1, 7, 21, 35, 1, 8, 28, 56, 35, 1, 9, 36, 84, 126, 1, 10, 45, 120, 210, 126, 1, 11, 55, 165, 330, 462, 1, 12, 66, 220, 495, 792, 462, 1, 13, 78, 286, 715, 1287, 1716, 1, 14, 91, 364, 1001, 2002, 3003, 1716, 1, 15, 105, 455, 1365, 3003, 5005
(list; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
The entry a(0,0) should actually be 1/2.
The row lengths of this array are [1,1,2,2,3,3,...]= A004526.
|
|
REFERENCES
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 795.
T. J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990. p. 54-5, Ex.1.5.31.
|
|
LINKS
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Index entries for sequences related to Chebyshev polynomials.
|
|
EXAMPLE
|
[1/2], [1], [1,2/2=1], [1,3], [1,4,6/2=3], [1,5,10], [1,6,15,20/2=10],...
|
|
CROSSREFS
|
Cf. A008311.
Bisection triangles: A122366 (odd numbered rows), A127673 (even numbered rows).
Sequence in context: A101038 A064883 A090844 this_sequence A104568 A030758 A104764
Adjacent sequences: A008311 A008312 A008313 this_sequence A008315 A008316 A008317
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
