computing the iterated exp(x)-1

[Gottfried]

It seems clear to me that these polynomials should be stored in a matrix. You have two sets of variables: n^0, n^1, n^2, ..., and z^0, z^1, z^2, ..., and a you have one coefficient for each combination, so long as the degree of n is less than the degree of z.

Jay, I'd like to check around with this matrix. I was starting to manually extract the coefficients... but this is tedious and I'm not sure about some signs, where the regularity breaks.
Could you provide this matrix, possibly some more rows, in a comma-separated format? Also, I reorder this coefficients for increasing powers of n, including zeros for nonoccurence of the specific coefficient,
so for instance I can write
M * V(n)
where M is the matrix of coefficients and V(n) is the vector of powers of n
V(n) = colvec(1,n,n^2,n^3,n^4,...). I can then try with M, similarity scalings, inverse, powers, logs, etc.

What I have now is

Code:

1,
0,   1,
0, -1/3,         1,
0,  1/6,       -5/6,       1,
0, -4/45,       2/3,     -13/9,     1,
0, 11/270,    -91/180,    89/54,  -77/36,   1,
0, -1/105,     91/270,  -149/90,  175/54,  -29/10,  1,
0, -11/1890,  -43/252,   391/270, -37/9,   1501/270, 223/60,  1

Gottfried