OFFSET
1,3
COMMENTS
LINKS
Wolfdieter Lang, First 7 rows.
FORMULA
a(n, m)= D(n)*((-1)^(n-m))*(fallfac(m+3, 4)^(n-1))/(product(fallfac(m+3, 4)-fallfac(r+3, 4), r=1..m-1)*product(fallfac(r+3, 4)-fallfac(m+3, 4), r=m+1..n)), with D(n) := A089516(n) and fallfac(n, m) := A008279(n, m) (falling factorials), 1<=m<=n else 0. (Replace in the denominator the first product by 1 if m=1 and the second one by 1 if m=n.)
EXAMPLE
Triangle begins:
1;
-1, 5;
1, -35, 90;
-3, 595,-6885, 12005;
...
A090215(2+3,3) = 199296 = (1*(4*3*2*1)^2 - 35*(5*4*3*2)^2 + 90*(6*5*4*3)^2)/56.
a(3,2)= -35 = 56*(-1)*((5*4*3*2)^2)/((5*4*3*2-4*3*2*1)*(6*5*4*3-5*4*3*2)).
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Dec 01 2003
STATUS
approved