|
Search: id:A034869
|
|
|
| A034869 |
|
Right half of Pascal's triangle. |
|
+0
5
|
|
| 1, 1, 2, 1, 3, 1, 6, 4, 1, 10, 5, 1, 20, 15, 6, 1, 35, 21, 7, 1, 70, 56, 28, 8, 1, 126, 84, 36, 9, 1, 252, 210, 120, 45, 10, 1, 462, 330, 165, 55, 11, 1, 924, 792, 495, 220, 66, 12, 1, 1716, 1287, 715, 286, 78, 13, 1, 3432, 3003, 2002, 1001, 364, 91, 14, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Comments from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 13 2006: "Also flattened table of the expansion coefficients of x^n in Chebyshev Polynomials T_k(x) of the first kind:
"x^n is 2^(1-n) multiplied by the sum of floor(1+n/2) terms using only terms T_k(x) with even k if n even, only terms T_k(x) with odd k if n is odd, and halving the coefficient a(..) in front of any T_0(x):
"x^0=2^(1-0) a(0)/2 T_0(x)
"x^1=2^(1-1) a(1) T_1(x)
"x^2=2^(1-2) [a(2)/2 T_0(x)+a(3) T_2(x)]
"x^3=2^(1-3) [a(4) T_1(x)+a(5) T_3(x)]
"x^4=2^(1-4) [a(6)/2 T_0(x)+a(7) T_2(x) +a(8) T_4(x)]
"x^5=2^(1-5) [a(9) T_1(x)+a(10) T_3(x) +a(11) T_5(x)]
"x^6=2^(1-6) [a(12)/2 T_0(x)+a(13) T_2(x) +a(14) T_4(x) +a(15) T_6(x)]
"x^7=2^(1-7) [a(16) T_1(x)+a(17) T_3(x) +a(18) T_5(x) +a(19) T_7(x)]"
|
|
MAPLE
|
for n from 0 to 60 do for j from n mod 2 to n by 2 do print( binomial(n, (n-j)/2) ); od; od; (Mathar)
|
|
CROSSREFS
|
Cf. A007318.
Sequence in context: A034850 A140352 A082588 this_sequence A053222 A129646 A058036
Adjacent sequences: A034866 A034867 A034868 this_sequence A034870 A034871 A034872
|
|
KEYWORD
|
nonn,tabl,easy
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
