A112517 Riordan array (1, x*(1+x)*(1-x*(1+x))).

1, 0, 1, 0, 0, 1, 0, -2, 0, 1, 0, -1, -4, 0, 1, 0, 0, -2, -6, 0, 1, 0, 0, 4, -3, -8, 0, 1, 0, 0, 4, 12, -4, -10, 0, 1, 0, 0, 1, 12, 24, -5, -12, 0, 1, 0, 0, 0, -5, 24, 40, -6, -14, 0, 1, 0, 0, 0, -12, -26, 40, 60, -7, -16, 0, 1, 0, 0, 0, -6, -48, -70, 60, 84, -8, -18, 0, 1, 0, 0, 0, -1, -8, -120, -145, 84, 112, -9, -20, 0, 1

Offset: 0

Author

Paul Barry, Sep 09 2005

Keywords

• easy
• sign
• tabl

Comments

Riordan array product (1, x*(1+x))*(1, x*(1-x)). Row sums are A112518. Inverse is A112519.

Examples

			Triangle begins:
  1;
  0,  1;
  0,  0,  1;
  0, -2,  0,  1;
  0, -1, -4,  0, 1;
  0,  0, -2, -6, 0, 1;
  ...
		

Crossrefs

Cf. A112518, A112519.

Programs

Mathematica

T[n_,k_]:=SeriesCoefficient[(x(1+x)(1-x(1+x)))^k,{x,0,n}]; Table[T[n,k],{n,0,12},{k,0,n}]//Flatten (* Stefano Spezia, Jun 08 2024 *)

Formula

Riordan array (1, x*(1-2*x^2-x^3)).

T(n, k) = Sum_{j=0..n} C(j, n-j)*C(k, j-k)*(-1)^(j-k).