A141343 Riordan array (1,x/sqrt(2-sqrt(1+4x))).

1, 0, 1, 0, 2, 1, 0, 2, 4, 1, 0, 4, 8, 6, 1, 0, 2, 16, 18, 8, 1, 0, 12, 24, 44, 32, 10, 1, 0, -12, 48, 90, 96, 50, 12, 1, 0, 72, 48, 180, 240, 180, 72, 14, 1, 0, -190, 160, 308, 544, 530, 304, 98, 16, 1, 0, 700, -40, 600, 1120, 1372, 1032, 476, 128

Offset: 0

Author

Paul Barry, Jun 26 2008

Keywords

• easy
• sign
• tabl

Comments

Factorizes as (1,xc(-x))*(1,x(1+x)/(1-2x)) where c(x) is the g.f. of A000108.

Row sums are A141344.

Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 2, -1, -1, -1, -1, -1, -1, -1, ...] DELTA [1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 15 2008

Examples

			Triangle begins
1,
0, 1,
0, 2, 1,
0, 2, 4, 1,
0, 4, 8, 6, 1,
0, 2, 16, 18, 8, 1,
0, 12, 24, 44, 32, 10, 1,
0, -12, 48, 90, 96, 50, 12, 1