A137423 Triangle T(n,k) = A053120(n,k)+binomial(n,k) read by rows, 0<=k<=n.

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, 0, 21, 91, 35, -91, 7, 65, 2, 8, -4, 56, 230, 56, -228, 8, 129, 1, 18, 36, -36, 126, 558, 84, -540, 9, 257, 0, 10, 95, 120, -190, 252, 1330, 120, -1235, 10, 513

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Apr 16 2008

Keywords

• tabl
• sign

Examples

			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, 0, 21, 91, 35, -91, 7, 65;
2, 8, -4, 56, 230, 56, -228, 8, 129;
1, 18, 36, -36, 126, 558, 84, -540, 9, 257;
0, 10, 95, 120, -190, 252, 1330, 120, -1235, 10, 513;
		

Crossrefs

Cf. A053120, A000051 (row sums and diagonal)

Programs

Maple

A137423 := proc(n,k)
    A053120(n,k)+binomial(n,k)
end proc: # R. J. Mathar, Sep 10 2013

Mathematica

(* 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]