A137423 - OEIS

%I #8 Sep 10 2013 12:05:21

%S 2,1,2,0,2,3,1,0,3,5,2,4,-2,4,9,1,10,10,-10,5,17,0,6,33,20,-33,6,33,1,

%T 0,21,91,35,-91,7,65,2,8,-4,56,230,56,-228,8,129,1,18,36,-36,126,558,

%U 84,-540,9,257,0,10,95,120,-190,252,1330,120,-1235,10,513

%N Triangle T(n,k) = A053120(n,k)+binomial(n,k) read by rows, 0<=k<=n.

%e 2;

%e 1, 2;

%e 0, 2, 3;

%e 1, 0, 3, 5;

%e 2, 4, -2, 4, 9;

%e 1, 10, 10, -10, 5, 17;

%e 0, 6, 33, 20, -33, 6, 33;

%e 1, 0, 21, 91, 35, -91, 7, 65;

%e 2, 8, -4, 56, 230, 56, -228, 8, 129;

%e 1, 18, 36, -36, 126, 558, 84, -540, 9, 257;

%e 0, 10, 95, 120, -190, 252, 1330, 120, -1235, 10, 513;

%p A137423 := proc(n,k)

%p     A053120(n,k)+binomial(n,k)

%p end proc: # _R. J. Mathar_, Sep 10 2013

%t (* Chebyshev A053120 polynomials*) (* addition of coefficients of Polynomials*) Q[x, 0] = 2; Q[x, 1] = x + 1 + ChebyshevT[1, x]; Q[x_, n_] := (x + 1)^n + ChebyshevT[n, x]; Table[ExpandAll[Q[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a0]

%Y Cf. A053120, A000051 (row sums and diagonal)

%K tabl,sign

%O 0,1

%A _Roger L. Bagula_ and _Gary W. Adamson_, Apr 16 2008