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%I #10 Mar 30 2012 18:59:02
%S 1,2,1,2,3,1,2,7,4,1,2,18,14,5,1,2,47,52,23,6,1,2,123,194,110,34,7,1,
%T 2,322,724,527,198,47,8,1,2,843,2702,2525,1154,322,62,9,1,2,2207,
%U 10084,12098,6726,2207,488,79,10,1,2,5778,37634,57965,39202,15127,3842,702,98
%N A number triangle associated with the Chebyshev polynomials of the first kind.
%C Row sums are A101162. Diagonal sums are A101163.
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F Number triangle S(n, k)=if(n=k, 1, 2T(n-k, (k+2)/2)) where T(n, k)=(n/2)sum{j=0..floor(n/2), C(n-j, j)(-1)^j*(2k)^(n-2j)};or S(n, k)=if(k<n, sum{j=0..n, C(n-k+j, 2j)(2(n-k)/(n-k+j))k^j}, if(k=n, 1, 0)) Columns have g.f. (1-x^2)x^k/(1-(k+2)x+x^2). Also square array if(n=0, 1, 2T(n, (k+2)/2) read by antidiagonals.
%e Rows begin {1}, {2,1}, {2,3,1}, {2,7,4,1}, {2,18,14,5,1},...
%e As a square array, rows begin
%e 1,1,1,1,1,...
%e 2,3,4,5,6,...
%e 2,7,14,23,34,...
%e 2,18,52,110,198,...
%e 2,47,194,527,1154,...
%K easy,nonn,tabl
%O 0,2
%A _Paul Barry_, Dec 02 2004
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