%I A101124
%S A101124 1,0,1,1,1,1,0,1,2,1,1,1,7,3,1,0,1,26,17,4,1,1,1,97,99,31,5,1,0,1,362,
               577,244,49,6,1,
%T A101124 1,1,1351,3363,1921,485,71,7,1,0,1,5042,19601,15124,4801,846,97,8,1,1,
               1,18817,114243,
%U A101124 119071,47525,10081,1351,127,9,1,0,1,70226,665857,937444,470449,120126,
               18817,2024,161
%V A101124 1,0,1,-1,1,1,0,1,2,1,1,1,7,3,1,0,1,26,17,4,1,-1,1,97,99,31,5,1,0,1,362,
               577,244,49,6,1,
%W A101124 1,1,1351,3363,1921,485,71,7,1,0,1,5042,19601,15124,4801,846,97,8,1,-1,
               1,18817,114243,
%X A101124 119071,47525,10081,1351,127,9,1,0,1,70226,665857,937444,470449,120126,
               18817,2024,161
%N A101124 Number triangle associated to Chebyshev polynomials of first kind.
%H A101124 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A101124 Number triangle S(n, k)=T(n-k, k), k<n, S(n, n)=1, 0 otherwise, where 
               T(n, k)=(n/2)sum{j=0..floor(n/2), C(n-j, j)(-1)^j*(2k)^(n-2j)}; Columns 
               have g.f. x^k(1-kx)/(1-2kx+x^2). Also, square array if(n=0, 1, T(n, 
               k)) read by anti-diagonals.
%e A101124 As a number triangle, rows begin {1}, {0,1}, {-1,1,1}, {0,1,2,1},...
%e A101124 As a square array, rows begin
%e A101124 1,1,1,1,1,...
%e A101124 0,1,2,3,4,...
%e A101124 -1,1,7,17,31,...
%e A101124 0,1,26,99,244,...
%e A101124 1,1,97,577,1921,..
%Y A101124 Columns include A001075, A001541, A001091, A001079, A023038, A011943. 
               Row sums are A101125. Diagonal sums are A101126.
%Y A101124 Cf. A053120.
%Y A101124 Sequence in context: A049270 A025269 A137296 this_sequence A011127 A157117 
               A061538
%Y A101124 Adjacent sequences: A101121 A101122 A101123 this_sequence A101125 A101126 
               A101127
%K A101124 easy,sign,tabl
%O A101124 0,9
%A A101124 Paul Barry (pbarry(AT)wit.ie), Dec 02 2004