%I A100258
%S A100258 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,
%T A100258 35,0,315,0,693,0,429,35,0,1260,0,6930,0,12012,0,6435,0,315,0,4620,0,
%U A100258 18018,0,25740,0,12155,63,0,3465,0,30030,0,90090,0
%V A100258 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,
%W A100258 0,-693,0,429,35,0,-1260,0,6930,0,-12012,0,6435,0,315,0,-4620,0,18018,
               0,-25740,0,12155,
%X A100258 -63,0,3465,0,-30030,0,90090,0
%N A100258 Triangle of coefficients of normalized Legendre polynomials, with increasing 
               exponents.
%D A100258 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 A100258 T. D. Noe, <a href="b100258.txt">Rows n=0..100 of triangle, flattened</
               a>
%H A100258 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].
%e A100258 1,
%e A100258 0,1,
%e A100258 -1,0,3,
%e A100258 0,-3,0,5,
%e A100258 3,0,-30,0,35,
%e A100258 0,15,0,-70,0,63,
%e A100258 -5,0,105,0,-315,0,231,
%e A100258 0,-35,0,315,0,-693,0,429,
%e A100258 35,0,-1260,0,6930,0,-12012,0,6435,
%o A100258 (PARI) a(k,n)=polcoeff(pollegendre(k,x),n)*2^valuation(k!,2)
%Y A100258 Without zeros: A008316. Row sums are A060818.
%Y A100258 Columns (with interleaved zeros and signs) include A001790, A001803, 
               A100259. Diagonals include A001790, A001800, A001801, A001802.
%Y A100258 Sequence in context: A021037 A053387 A141030 this_sequence A045763 A132748 
               A055945
%Y A100258 Adjacent sequences: A100255 A100256 A100257 this_sequence A100259 A100260 
               A100261
%K A100258 sign,tabl
%O A100258 0,6
%A A100258 Ralf Stephan, Nov 13 2004
%E A100258 Triangle begins: