A167655 Riordan array (1-u,u) where u=x/(1+x+x^2).

1, -1, 1, 1, -2, 1, 0, 2, -3, 1, -1, 0, 4, -4, 1, 1, -3, -1, 7, -5, 1, 0, 4, -6, -4, 11, -6, 1, -1, -1, 11, -9, -10, 16, -7, 1, 1, -4, -6, 24, -10, -20, 22, -8, 1, 0, 6, -9, -21, 44, -6, -35, 29, -9, 1, -1, -2, 21, -12, -55, 70, 7, -56, 37, -10, 1

Offset

0,5

Comments

Inverse of Riordan array A167630. Row sums : A000007.

Links

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

Formula

T(n,k) = T(n-1,k-1) - T(n-1,k) - T(n-2,k), T(0,0) = T(1,1) = T(2,0) = T(2,2) = 1, T(1,0) = -1, T(2,1) = -2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 22 2014

Example

Triangle begins:
1;
-1, 1;
1, -2, 1;
0, 2, -3, 1;
-1, 0, 4, -4, 1;
1, -3, -1, 7, -5, 1;
0, 4, -6, -4, 11, -6, 1;
-1, -1, 11, -9, -10, 16, -7, 1;
1, -4, -6, 24, -10, -20, 22, -8, 1;
0, 6, -9, -21, 44, -6, -35, 29, -9, 1;
-1, -2, 21, -12, -55, 70, 7, -56, 37, -10, 1;
... Philippe Deléham, Jan 22 2014

Crossrefs

Cf. A000124

Sequence in context: A236358 A144082 A145579 * A346148 A262781 A157218

Adjacent sequences: A167652 A167653 A167654 * A167656 A167657 A167658

Keyword

sign,tabl

Author

Philippe Deléham, Nov 08 2009

Status

approved