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Search: id:A008316
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| A008316 |
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Triangle of coefficients of Legendre polynomials P_n (x). |
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+0
5
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| 1, 1, -1, 3, -3, 5, 3, -30, 35, 15, -70, 63, -5, 105, -315, 231, -35, 315, -693, 429, 35, -1260, 6930, -12012, 6435, 315, -4620, 18018, -25740, 12155, -63, 3465, -30030, 90090, -109395, 46189, -693, 15015, -90090, 218790, -230945, 88179, 231, -18018, 225225, -1021020, 2078505, -1939938, 676039
(list; graph; listen)
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OFFSET
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0,4
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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].
Eric Weisstein's World of Mathematics, Legendre Polynomial
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EXAMPLE
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1; 1; -1,3; -3,5; 3,-30,35; 15,-70,63; ...
P_6(x) = (-5+105x^2-315x^4+231x^6)/16 so T(6,)=-5,105,-315,231.
P_5(x) = (15x-70x^3+63x^5)/8 so T(5,)=15,-70,63.
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MATHEMATICA
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Flatten[Table[(LegendreP[i, x]/.{Plus->List, x->1})Max[ Denominator[LegendreP[i, x]/.{Plus->List, x->1}]], {i, 0, 12}]]
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PROGRAM
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(PARI) T(n, k)=if(n<0, 0, polcoeff(pollegendre(n)*2^valuation((n\2*2)!, 2), n%2+2*k))
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CROSSREFS
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Cf. A001790, A001800, A001801.
With zeros: A100258.
Adjacent sequences: A008313 A008314 A008315 this_sequence A008317 A008318 A008319
Sequence in context: A071053 A094439 A122037 this_sequence A072820 A131950 A116192
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KEYWORD
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sign,tabf,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 28 2002
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