OFFSET
0,5
FORMULA
T(n, k) = T(n-1, k) - A060083(n-1, k-1), for n>0, with T(0, 0)=1.
EXAMPLE
T(5,3) = -10 = T(4,3) - A060083(4,2) = 4 - 14.
T(6,2) = -229 = T(5,2) - A060083(5,1) = 26 - 255.
Rows begin:
[1],
[1,1],
[1,2,1],
[1,1,3,1],
[1,4,-2,4,1],
[1,-13,26,-10,5,1],
[1,142,-229,116,-25,6,1],
[1,-1931,3181,-1567,371,-49,7,1],
[1,36296,-59700,29464,-6922,952,-84,8,1],...
The matrix inverse is equal to A060083:
[1],
[ -1,1],
[1,-2,1],
[ -3,5,-3,1],
[17,-28,14,-4,1],
[ -155,255,-126,30,-5,1],...
PROG
(PARI) {T(n, k)=local(M=matrix(n+1, n+1)); M[1, 1]=1; if(n>0, M[2, 1]=1; M[2, 2]=1); for(r=3, n+1, for(c=1, r, M[r, c]=if(c==1, M[r-1, 1], if(c==r, 1, M[r, c]=M[r-1, c]-((matrix(r-1, r-1, i, j, M[i, j]))^-1)[r-1, c-1])))); return(M[n+1, k+1])}
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Dec 28 2004
STATUS
approved