A165621 -id:A165621 - cp's OEIS frontend

A165620 Riordan array ((1-x)/(1-x^4),x/(1+x^2)).

1, -1, 1, 0, -1, 1, 0, -1, -1, 1, 1, 1, -2, -1, 1, -1, 2, 2, -3, -1, 1, 0, -2, 4, 3, -4, -1, 1, 0, -2, -4, 7, 4, -5, -1, 1, 1, 2, -6, -7, 11, 5, -6, -1, 1, -1, 3, 6, -13, -11, 16, 6, -7, -1, 1, 0, -3, 9, 13, -24, -16, 22, 7, -8, -1, 1

Offset: 0

Paul Barry, Sep 22 2009

Diagonal sums are (-1)^n. Row sums have g.f. 1/(1+x^3).
The transform of the aerated Catalan numbers by this matrix is (-1)^n.
The transform of the shifted central binomial coefficient C(n+1,floor((n+1)/2)) is 1^n.
Factorizes as (1/(1+x),x)*(1/(1+x^2),x/(1+x^2)). Inverse is A165621.

			Triangle begins
1,
-1, 1,
0, -1, 1,
0, -1, -1, 1,
1, 1, -2, -1, 1,
-1, 2, 2, -3, -1, 1,
0, -2, 4, 3, -4, -1, 1,
0, -2, -4, 7, 4, -5, -1, 1,
1, 2, -6, -7, 11, 5, -6, -1, 1,
-1, 3, 6, -13, -11, 16, 6, -7, -1, 1

P. Barry, Symmetric Third-Order Recurring Sequences, Chebyshev Polynomials, and Riordan Arrays, JIS 12 (2009) 09.8.6.

(* The function RiordanArray is defined in A256893. *)
RiordanArray[(1 - #)/(1 - #^4)&, #/(1 + #^2)&, 11] // Flatten (* Jean-François Alcover, Jul 16 2019 *)

Number triangle T(n,k)=sum{j=0..n, (-1)^(n-j)(-1)^((j-k)/2)(1+(-1)^(j-k))C((j+k)/2,k)/2}.

cp's OEIS Frontend

A165620 Riordan array ((1-x)/(1-x^4),x/(1+x^2)).

Views

Author

Keywords

Comments

Examples

Links

Programs

Mathematica

Formula