OFFSET
0,4
COMMENTS
The column sequences are derived from the logarithm of a factorial series (cf. A111537).
FORMULA
T(n, n)=1 and T(n+1, n)=n+1, else T(n+k+1, k) = -A111537(k) for k>=1.
EXAMPLE
Triangle begins:
1;
-1,1;
-2,-2,1;
-8,-2,-3,1;
-44,-8,-2,-4,1;
-296,-44,-8,-2,-5,1;
-2312,-296,-44,-8,-2,-6,1;
-20384,-2312,-296,-44,-8,-2,-7,1;
-199376,-20384,-2312,-296,-44,-8,-2,-8,1; ...
After initial terms, all columns are equal to -A111537.
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(n==k, 1, if(n==k+1, -n, -(n-k-1)*polcoeff(log(sum(i=0, n, (i+1)!/1!*x^i)), n-k-1))))
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Aug 06 2005
STATUS
approved