OFFSET
0,2
COMMENTS
The sequence a(m) is also the expansion of (1-x^n)/(1-x-2x^n+x^{n+1}).
Instead of b(i) = a(n*i) one can take b(i) = a(n*i+p) for p=1..n-1.
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
From Alois P. Heinz, Jul 16 2009: (Start)
T(n,k) = (-1)^k/(k+1)! * (1+k+(n-k)*2^(k+1)) * Product_{j=1..k}(n+j-k).
G.f. of column k: (-1)^k * x^k * (1+(2^(k+1)-1)*x)/(1-x)^(k+2). (End)
EXAMPLE
For n=5 (A113444) the recurrence relation is b(i) = 11b(i-1)-45b(i-2) +90b(i-3)-90b(i-4)+37b(i-5)-b(i-6), so the fifth row reads 11, -45, 90, -90, 37, -1.
MAPLE
T:= (n, k)-> (-1)^k /(k+1)! *(1+k +(n-k) *2^(k+1)) *mul (n+j-k, j=1..k):
seq(seq(T(n, k), k=0..n), n=0..11); # Alois P. Heinz, Jul 16 2009
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Floor van Lamoen, Nov 04 2005
EXTENSIONS
More terms from Alois P. Heinz, Jul 16 2009
STATUS
approved