%I A100257
%S A100257 1,1,0,1,0,1,1,0,3,0,1,0,4,0,3,1,0,5,0,10,0,1,0,6,0,15,0,10,1,0,7,0,21,
%T A100257 0,35,0,1,0,8,0,28,0,56,0,35,1,0,9,0,36,0,84,0,126,0,1,0,10,0,45,0,120,
%U A100257 0,210,0,126,1,0,11,0,55,0,165,0,330,0,462,0,1,0,12,0,66,0,220,0
%N A100257 Triangle of expansions of 2^(k-1)*x^k in terms of T(n,x), in descending 
               degrees n of T, with T the Chebyshev polynomials.
%D A100257 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 795.
%H A100257 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 A100257 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%e A100257 x^0 = T(0,x)
%e A100257 x^1 = T(1,x) + 0T(0,x)
%e A100257 2x^2 = T(2,x) + 0T(1,x) + 1T(0,x)
%e A100257 4x^3 = T(3,x) + 0T(2,x) + 3T(1,x) + 0T(0,x)
%e A100257 8x^4 = T(4,x) + 0T(3,x) + 4T(2,x) + 0T(1,x) + 3T(0,x)
%e A100257 16x^5 = T(5,x) + 0T(4,x) + 5T(3,x) + 0T(2,x) + 10T(1,x) + 0T(0,x)
%o A100257 (PARI) a(k,n)=if(k==1,1,if(n%2==0||k<0||n>k,0,if(n>=k-1,binomial(2*floor(k/
               2),floor(k/2))/2,binomial(k-1,floor(n/2)))))
%Y A100257 Without zeros: A008311. Row sums are A011782. Cf. A092392.
%Y A100257 Diagonals are (with interleaved zeros) twice A001700, A001791, A002054, 
               A002694, A003516, A002696, A030053, A004310, A030054, A004311, A030055, 
               A004312, A030056, A004313.
%Y A100257 Sequence in context: A117178 A111527 A035695 this_sequence A100573 A049087 
               A046665
%Y A100257 Adjacent sequences: A100254 A100255 A100256 this_sequence A100258 A100259 
               A100260
%K A100257 nonn,tabl
%O A100257 0,9
%A A100257 Ralf Stephan, Nov 13 2004