Search: id:A008317
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%I A008317
%S A008317 1,1,1,2,3,2,7,20,8,27,28,8,33,110,72,16,143,182,88,16,715,2600,2160,
%T A008317 832,128,3315,4760,2992,960,128,4199,16150,15504,7904,2176,256,20349,
%U A008317 31654,23408,10080,2432,256,52003,208012,220248,133952,50048,10752
%N A008317 Triangle of coefficients of expansions of powers of x in terms of Legendre 
               polynomials P_n(x) over common denominator.
%D A008317 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.
%D A008317 P. J. Davis, Interpolation and Approximation, Dover Publications, 1975, 
               p. 372.
%H A008317 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 A008317 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LegendrePolynomial.html">Legendre Polynomial</a>
%e A008317 {1},{1},{1,2},{3,2},{7,20,8},{27,28,8},{33,110,72,16},...
%e A008317 x^5 = (27P_1+28P_3+8P_5)/63, so T(5,2)=8.
%o A008317 (PARI) T(n,m)=local(Q);if(n<0,0,m=n%2+m*2;Q=intformal(x^n*pollegendre(m));
               (subst(Q,x,1)-subst(Q,x,-1))*(2*m+1)/2*polcoeff(pollegendre(n),n)*2^valuation((n\2*2)!,
               2))
%Y A008317 A001790 is common denominator.
%Y A008317 Sequence in context: A122076 A014784 A048601 this_sequence A139011 A152297 
               A063708
%Y A008317 Adjacent sequences: A008314 A008315 A008316 this_sequence A008318 A008319 
               A008320
%K A008317 nonn,tabl
%O A008317 0,4
%A A008317 N. J. A. Sloane (njas(AT)research.att.com).

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