OFFSET
0,2
COMMENTS
Row sums are (1,-1,0,0,0,...) = 2*C(0,n) - C(1,n).
Diagonal sums are -2*0^n - F(n-4) with g.f. (1 - 3x + 2x^2) / (1 - x - x^2).
Inverse of A113310.
FORMULA
T(n, k) = C(n-1, n-k) - 2*C(n-2, n-k-1).
exp(x) * e.g.f. for row n = e.g.f. for diagonal n. For example, for n = 3 we have exp(x)*(-x + x^3/3!) = -x - 2*x^2/2! - 2*x^3/3! + 5*x^5/5! + .... The same property holds more generally for Riordan arrays of the form ( f(x), x/(1 - x) ). - Peter Bala, Dec 21 2014
EXAMPLE
The triangle T(n, k) begins:
n\k 0 1 2 3 4 5 6 7 8 9 10 ...
0: 1
1: -2 1
2: 0 -1 1
3: 0 -1 0 1
4: 0 -1 -1 1 1
5: 0 -1 -2 0 2 1
6: 0 -1 -3 -2 2 3 1
7: 0 -1 -4 -5 0 5 4 1
8: 0 -1 -5 -9 -5 5 9 5 1
9: 0 -1 -6 -14 -14 0 14 14 6 1
10: 0 -1 -7 -20 -28 -14 14 28 20 7 1
... Reformatted. - Wolfdieter Lang, Jan 06 2015
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Oct 25 2005
STATUS
approved