A145316 L-matrix for Hankel matrix of aerated factorials.

1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 4, 0, 1, 0, 6, 0, 6, 0, 1, 6, 0, 18, 0, 9, 0, 1, 0, 24, 0, 36, 0, 12, 0, 1, 24, 0, 96, 0, 72, 0, 16, 0, 1, 0, 120, 0, 240, 0, 120, 0, 20, 0, 1, 120, 0, 600, 0, 600, 0, 200, 0

Offset: 0

Author

Paul Barry, Oct 07 2008

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A056953. Hankel matrix of aerated factorials H=LDU where U=transpose of L. Aerated version of A104557.

Examples

			Triangle begins 1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 4, 0, 1, 0, 6, 0, 6, 0, 1, 6, 0, 18, 0, 9, 0, 1, 0, 24, 0, 36, 0, 12, 0, 1, 24, 0, 96, 0, 72, 0, 16, 0, 1
		

Formula

Triangle T(n,k)=[k<=n]((n-k)/2)!C((n+k)/2-floor(k/2),floor((k+1)/2))C((n+k)/2-floor((k+1)/2),floor(k/2))(1+(-1)^(n-k))/2;