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%I #15 Aug 07 2014 11:36:52
%S 1,1,0,2,0,1,4,0,3,0,8,0,8,0,1,16,0,20,0,5,0,32,0,48,0,18,0,1,64,0,
%T 112,0,56,0,7,0,128,0,256,0,160,0,32,0,1,256,0,576,0,432,0,120,0,9,0,
%U 512,0,1280,0,1120,0,400,0,50,0,1,1024,0,2816,0,2816,0,1232,0,220
%N Triangle of coefficients of the polynomials a(n, x) = 2*a(n-1, x)+ x^2*a(n-2,x), n >= 1, a(0, x) = 1, a(1, x) = 1.
%C Unsigned Chebyshev numbers of the first kind. Columns include A011782, A001792, A001793, A001794, A006974.
%C For the Riordan coefficient triangle for Chebyshev's T-polynomials (decreasing odd or even powers of x) see A039991. - _Wolfdieter Lang_, Aug 06 2014
%F T(n,k) = [x^k] a(n,x), k = 0, 1, ..., n, with polynomial a(n,x) defined by the recurrence given as name. Its Binet-de Moivre form is a(n, x) = ((1+sqrt(x^2+1))^n + (1-sqrt(x^2+1))^n)/2.
%F O.g.f. for row polynomials a(n,x): (1-z)/(1 - 2*z - (x*z)^2). Compare with A039991.
%e Triangle rows are {1}, {1,0}, {2,0,1}, {4,0,3,0}, {8,0,8,0,1},.... [Corrected by _Philippe Deléham_, Dec 27 2007]
%e See the unsigned example under A039991. - _Wolfdieter Lang_, Aug 06 2014
%Y Cf. A008310, A039991 (signed).
%K easy,nonn,tabl
%O 0,4
%A _Paul Barry_, Mar 15 2003
%E Edited. Name and formula clarified. G.f. of row polynomial, and crossref. A039991 added. - _Wolfdieter Lang_, Aug 06 2014
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