A228356 - OEIS

%I #22 Jun 11 2017 18:54:18

%S 1,1,1,-1,3,1,-1,5,5,1,1,7,19,7,1,1,9,71,41,9,1,-1,11,265,239,71,11,1,

%T -1,13,989,1393,559,109,13,1,1,15,3691,8119,4401,1079,155,15,1,1,17,

%U 13775,47321,34649,10681,1847,209,17,1

%N The triangle associated with the family of polynomials W_n(x).

%C W_n(x) is the family of polynomials in x with integer coefficients given by W_n(x) = sin((2n+1)arccos(x)/2)/(sin(arccos(x)/2)).

%C These polynomials are intimately linked with the Chebyshev polynomials of the first and second kinds, and represent the polynomials associated with the Dirichlet kernel.

%F W_{n+1} = 2xW_n(x) - W_{n-1}, W_0(x)=1, W_1(x)=2x+1.

%e The triangle is given here as W_0(0)=1, W_1(0)=1, W_0(1)=1, W_2(0)=-1, W_1(1)=3, W_0(2)=1, W_3(0)=-1, W_2(1)=5 ...

%t W[0, _] = 1; W[1, x_] := 2 x + 1; W[n_, x_] := W[n, x] = 2 x W[n - 1, x] - W[n - 2, x]; Table[W[n - x, x] , {n, 0, 9}, {x, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 11 2017 *)

%Y Cf. A028297, A101124, A133156, A228161, A228565, A228637, A180870.

%K sign,easy,tabl

%O 0,5

%A _Jonny Griffiths_, Aug 28 2013