Search: id:A008316
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%I A008316
%S A008316 1,1,1,3,3,5,3,30,35,15,70,63,5,105,315,231,35,315,693,429,35,1260,6930,
%T A008316 12012,6435,315,4620,18018,25740,12155,63,3465,30030,90090,109395,46189,
               693,
%U A008316 15015,90090,218790,230945,88179,231,18018,225225,1021020,2078505,1939938,
               676039
%V A008316 1,1,-1,3,-3,5,3,-30,35,15,-70,63,-5,105,-315,231,-35,315,-693,429,35,
               -1260,6930,
%W A008316 -12012,6435,315,-4620,18018,-25740,12155,-63,3465,-30030,90090,-109395,
               46189,-693,
%X A008316 15015,-90090,218790,-230945,88179,231,-18018,225225,-1021020,2078505,
               -1939938,676039
%N A008316 Triangle of coefficients of Legendre polynomials P_n (x).
%D A008316 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.
%H A008316 T. D. Noe, <a href="b008316.txt">Rows n=0..100 of triangle, flattened</
               a>
%H A008316 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A008316 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LegendrePolynomial.html">Legendre Polynomial</a>
%e A008316 1; 1; -1,3; -3,5; 3,-30,35; 15,-70,63; ...
%e A008316 P_6(x) = (-5+105x^2-315x^4+231x^6)/16 so T(6,)=-5,105,-315,231.
%e A008316 P_5(x) = (15x-70x^3+63x^5)/8 so T(5,)=15,-70,63.
%t A008316 Flatten[Table[(LegendreP[i, x]/.{Plus->List, x->1})Max[ Denominator[LegendreP[i, 
               x]/.{Plus->List, x->1}]], {i, 0, 12}]]
%o A008316 (PARI) T(n,k)=if(n<0,0,polcoeff(pollegendre(n)*2^valuation((n\2*2)!,2),
               n%2+2*k))
%Y A008316 Cf. A001790, A001800, A001801.
%Y A008316 With zeros: A100258.
%Y A008316 Sequence in context: A071053 A094439 A122037 this_sequence A072820 A131950 
               A116192
%Y A008316 Adjacent sequences: A008313 A008314 A008315 this_sequence A008317 A008318 
               A008319
%K A008316 sign,tabf,easy,nice
%O A008316 0,4
%A A008316 N. J. A. Sloane (njas(AT)research.att.com).
%E A008316 More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 28 2002

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