A119830 Bi-diagonal inverse of (2n)!/(2k)!.

1, -2, 1, 0, -12, 1, 0, 0, -30, 1, 0, 0, 0, -56, 1, 0, 0, 0, 0, -90, 1, 0, 0, 0, 0, 0, -132, 1, 0, 0, 0, 0, 0, 0, -182, 1, 0, 0, 0, 0, 0, 0, 0, -240, 1, 0, 0, 0, 0, 0, 0, 0, 0, -306, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -380, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -462, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -552, 1, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Paul Barry, May 25 2006

Keywords

• easy
• sign
• tabl

Comments

Row sums are 1-2n(n-1)=1-b(n). Inverse of A119828.

Examples

			Triangle begins
1,
-2, 1,
0, -12, 1,
0, 0, -30, 1,
0, 0, 0, -56, 1,
0, 0, 0, 0, -90, 1,
0, 0, 0, 0, 0, -132, 1,
0, 0, 0, 0, 0, 0, -182, 1,
0, 0, 0, 0, 0, 0, 0, -240, 1,
0, 0, 0, 0, 0, 0, 0, 0, -306, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, -380, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -462, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -552, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -650, 1
		

Formula

Column k has g.f. x^k(1-b(k+1)x) where b(n)=2n(2n-1).