A281862 Riordan transform of the triangular number sequence A000217 with the Chebyshev S matrix A049310.

0, 1, 3, 4, 1, -6, -11, -6, 9, 21, 14, -12, -34, -25, 15, 50, 39, -18, -69, -56, 21, 91, 76, -24, -116, -99, 27, 144, 125, -30, -175, -154, 33, 209, 186, -36, -246, -221, 39, 286, 259, -42, -329, -300, 45, 375

Offset: 0

Author

Wolfdieter Lang, Feb 18 2017

Keywords

• sign
• easy

Comments

For the analogous sequence with the inverse S Riordan matrix A053121 see A189391.

Crossrefs

Cf. A000217, A049310, A128504, A189391.

Programs

Mathematica

CoefficientList[Series[x (1 + x^2)/(1 - x + x^2)^3, {x, 0, 45}], x] (* Michael De Vlieger, Feb 18 2017 *)

Formula

a(n) = Sum_{m=0..n} A049310(n,m)*A000217(m), n >= 0.

a(n) = b(n-1) + b(n-3), n >= 0 with b(-3) = b(-2) = b(-1) = 0 and b(n) = A128504(n) for n >= 0.

G.f.: (1/(1+x^2))*Tri(x/(1+x^2)), with Tri(x) = x/(1-x)^3 (g.f. of A000217).

G.f. x*(1 + x^2)/(1 - x + x^2)^3.