OFFSET
0,13
COMMENTS
Inverse is the unsigned version.
FORMULA
T(n,k)=[k<=n]*((1+(-1)^(n-k))/2)*((n-k)/2)!*C((n+k)/2-1-floor((k-1)/2), (n+k)/2-1-floor((k-1)/2)-floor(k/2))
*C((n+k)/2-1-floor(k/2),(n+k)/2-1-floor(k/2)-floor((k-1)/2))*(-1)^((n-k)/2).
EXAMPLE
Triangle begins
1,
0, 1,
0, 0, 1,
0, -1, 0, 1,
0, 0, -2, 0, 1,
0, 2, 0, -4, 0, 1,
0, 0, 6, 0, -6, 0, 1,
0, -6, 0, 18, 0, -9, 0, 1,
0, 0, -24, 0, 36, 0, -12, 0, 1,
0, 24, 0, -96, 0, 72, 0, -16, 0, 1,
0, 0, 120, 0, -240, 0, 120, 0, -20, 0, 1,
0, -120, 0, 600, 0, -600, 0, 200, 0, -25, 0, 1,
0, 0, -720, 0, 1800, 0, -1200, 0, 300, 0, -30, 0, 1
Product matrix of inverse is
0, 1,
0, 0, 1,
0, 1, 0, 1,
0, 0, 1, 0, 1,
0, 0, 0, 2, 0, 1,
0, 0, 0, 0, 2, 0, 1,
0, 0, 0, 0, 0, 3, 0, 1,
0, 0, 0, 0, 0, 0, 3, 0, 1,
0, 0, 0, 0, 0, 0, 0, 4, 0, 1
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, May 19 2010
STATUS
approved