|
| |
|
|
A100258
|
|
Triangle of coefficients of normalized Legendre polynomials, with increasing exponents.
|
|
9
| |
|
|
1, 0, 1, -1, 0, 3, 0, -3, 0, 5, 3, 0, -30, 0, 35, 0, 15, 0, -70, 0, 63, -5, 0, 105, 0, -315, 0, 231, 0, -35, 0, 315, 0, -693, 0, 429, 35, 0, -1260, 0, 6930, 0, -12012, 0, 6435, 0, 315, 0, -4620, 0, 18018, 0, -25740, 0, 12155, -63, 0, 3465, 0, -30030, 0, 90090, 0
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,6
|
|
|
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. 798.
|
|
|
LINKS
| T. D. Noe, Rows n=0..100 of triangle, flattened
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].
|
|
|
EXAMPLE
| 1,
0,1,
-1,0,3,
0,-3,0,5,
3,0,-30,0,35,
0,15,0,-70,0,63,
-5,0,105,0,-315,0,231,
0,-35,0,315,0,-693,0,429,
35,0,-1260,0,6930,0,-12012,0,6435,
|
|
|
PROG
| (PARI) a(k, n)=polcoeff(pollegendre(k, x), n)*2^valuation(k!, 2)
|
|
|
CROSSREFS
| Without zeros: A008316. Row sums are A060818.
Columns (with interleaved zeros and signs) include A001790, A001803, A100259. Diagonals include A001790, A001800, A001801, A001802.
Sequence in context: A053387 A141030 A194084 * A045763 A132748 A055945
Adjacent sequences: A100255 A100256 A100257 * A100259 A100260 A100261
|
|
|
KEYWORD
| sign,tabl
|
|
|
AUTHOR
| Ralf Stephan, Nov 13 2004
|
|
|
EXTENSIONS
| Triangle begins:
|
| |
|
|
