|
| |
|
|
A085841
|
|
Triangle: row #n has n+1 terms. T(n,m) = 4^m (2n+1)! / [ (2n-2m)! (2m+1)! ].
|
|
1
| |
|
|
1, 3, 4, 5, 40, 16, 7, 140, 336, 64, 9, 336, 2016, 2304, 256, 11, 660, 7392, 21120, 14080, 1024, 13, 1144, 20592, 109824, 183040, 79872, 4096, 15, 1820, 48048, 411840, 1281280, 1397760, 430080, 16384
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Row #n has the unsigned coefficients of a polynomial whose roots are 2 cot (pi k / (2n+1)) [for k=1 to 2n].
Polynomial of row #n = sum(m=0 to n) [(-1)^m] T(n,m) x^(2n-2m).
|
|
|
EXAMPLE
| 1
3x^2 - 4
5x^4 - 40x^2 + 16
7x^6 - 140x^4 + 336x^2 - 64
9x^8 - 336x^6 + 2016x^4 - 2304x^2 + 256
11x^10 - 660x^8 + 7392x^6 - 21120x^4 + 14080x^2 - 1024
Polynomial #4 has eight roots: 2 cot (pi k / 9) for k=1 to 8.
|
|
|
CROSSREFS
| Cf. A085840.
Sequence in context: A126896 A123957 A085285 * A163483 A004784 A024687
Adjacent sequences: A085838 A085839 A085840 * A085842 A085843 A085844
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 05 2003
|
|
|
EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), Nov 13 2005
|
| |
|
|
