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Search: id:A100258
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| A100258 |
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Triangle of coefficients of normalized Legendre polynomials, with increasing exponents. |
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+0
9
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| 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; listen)
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OFFSET
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0,6
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REFERENCES
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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.
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LINKS
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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].
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EXAMPLE
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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,
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PROGRAM
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(PARI) a(k, n)=polcoeff(pollegendre(k, x), n)*2^valuation(k!, 2)
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CROSSREFS
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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: A021037 A053387 A141030 this_sequence A045763 A132748 A055945
Adjacent sequences: A100255 A100256 A100257 this_sequence A100259 A100260 A100261
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KEYWORD
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sign,tabl
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AUTHOR
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Ralf Stephan, Nov 13 2004
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EXTENSIONS
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Triangle begins:
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