A112475 Riordan array (1/(1+x),x(1+x)/(1-x)).

1, -1, 1, 1, 1, 1, -1, 1, 3, 1, 1, 1, 5, 5, 1, -1, 1, 7, 13, 7, 1, 1, 1, 9, 25, 25, 9, 1, -1, 1, 11, 41, 63, 41, 11, 1, 1, 1, 13, 61, 129, 129, 61, 13, 1, -1, 1, 15, 85, 231, 321, 231, 85, 15, 1, 1, 1, 17, 113, 377, 681, 681, 377, 113, 17, 1

Offset

0,9

Comments

Equivalent to Delannoy triangle A008288 with prepended column 1,-1,1,-1,... Row sums are A111954. Diagonal sums are A112476. Inverse is A112477.

Links

Table of n, a(n) for n=0..65.

Formula

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

Example

Triangle starts:
   1;
  -1, 1;
   1, 1, 1;
  -1, 1, 3,  1;
   1, 1, 5,  5,  1;
  -1, 1, 7, 13,  7, 1;
   1, 1, 9, 25, 25, 9, 1;
  ...

Mathematica

T[n_, k_]:=SeriesCoefficient[(x(1+x)/(1-x))^k/(1+x), {x, 0, n}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* Stefano Spezia, May 26 2024 *)

Crossrefs

Cf. A008288, A111954, A112476, A112477.

Sequence in context: A348963 A350470 A277604 * A347232 A307855 A361277

Adjacent sequences: A112472 A112473 A112474 * A112476 A112477 A112478

Keyword

easy,sign,tabl

Author

Paul Barry, Sep 07 2005

Status

approved