cp's OEIS Frontend

A228637 The number triangle associated with the polynomials V_n(x).

%I A228637 #13 Jun 02 2025 08:37:36
%S A228637 1,-1,1,-1,1,1,1,1,3,1,1,1,11,5,1,-1,1,41,29,7,1,-1,1,153,169,55,9,1,
%T A228637 1,1,571,985,433,89,11,1,1,1,2131,5741,3409,881,131,13,1,-1,1,7953,
%U A228637 33461,26839,8721,1561,181,15,1
%N A228637 The number triangle associated with the polynomials V_n(x).
%C A228637 V(n) is the polynomial with integer coefficients in x given by cos((2n+1)(arccos(x)/2))/(arccos(x)/2). The triangle here is given by V_0(0), V_1(0), V_0(1),  V_2(0), V_1(1), V_0(2),  V_3(0), V_2(1), V_1(2), V_0(3), V_4(0),....
%F A228637 The terms are given by the recurrence relation  V_{n+1}(x) = 2xV_n(x)-V_{n-1}(x), V_0(x) = 1, V_1(x)=2x-1.
%e A228637 V_0(x)=1, V_1(x)=2x-1, V_2(x)=4x^2-2x-1,  ...
%Y A228637 Cf. A028297, A101124, A133156, A228161, A228565, A180870.
%K A228637 sign,tabl,easy
%O A228637 0,9
%A A228637 _Jonny Griffiths_, Aug 28 2013