OFFSET
0,2
COMMENTS
This is a simple Riordan array, an infinite lower triangular matrix. It is the inverse matrix of A130321 (with zeros above the diagonal).
Row sums have o.g.f. (1-2*x)/(1-x) and give 1, repeat(-1), i.e., A153881(n+1), n >= 0.
Alternate row sums have o.g.f. (1-2*x)/(1+x) and give 1, repeat(-3,3), i.e., (-1)^n*A122553(n).
FORMULA
T(n, k) = 0 if n < k and k = 0..(n-2) for n >= 2, and T(n, n) = 1 and T(n, n-1) = -2.
G.f. for row polynomials P(n, x) = -2^x^(n-1) + x^n is (1-2*z)/(1-x*z).
G.f. for k-th column: (1-2*x)*x^k, k >= 0.
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 -2 1
3: 0 0 -2 1
4: 0 0 0 -2 1
5: 0 0 0 0 -2 1
6: 0 0 0 0 0 -2 1
7: 0 0 0 0 0 0 -2 1
8: 0 0 0 0 0 0 0 -2 1
9: 0 0 0 0 0 0 0 0 -2 1
10: 0 0 0 0 0 0 0 0 0 -2 1
...
PROG
(Haskell)
a251635 n k = a251635_tabl !! n !! k
a251635_row n = a251635_tabl !! n
a251635_tabl = [1] : iterate (0 :) [-2, 1]
-- Reinhard Zumkeller, Jan 11 2015
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Jan 10 2015
STATUS
approved