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

0,8

Comments

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

Links

Table of n, a(n) for n=0..90.

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).

Example

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

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 *)

Crossrefs

Cf. A112518, A112519.

Sequence in context: A185370 A352747 A364955 * A112519 A276981 A230305

Adjacent sequences: A112514 A112515 A112516 * A112518 A112519 A112520

Keyword

easy,sign,tabl

Author

Paul Barry, Sep 09 2005

Status

approved