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- 1 x x^2 x^3 x^4 x^5 x^6 x^7
- ---------------------------------------------------------------
- 1 0 0 0 0 0 0 0 for f0(x)=1
- 1 1 0 0 0 0 0 0 for f1(x)=(x+1)^f0(x)
- 1 1 1 1/2 1/3 1/12 3/40 -1/120 for f2(x)=(x+1)^f1(x)
- 1 1 1 3/2 4/3 3/2 53/40 233/180
- 1 1 1 3/2 7/3 3 163/40 1861/360
- 1 1 1 3/2 7/3 4 243/40 3421/360
- 1 1 1 3/2 7/3 4 283/40 4321/360
- 1 1 1 3/2 7/3 4 283/40 4681/360
- 1 1 1 3/2 7/3 4 283/40 4681/360
- 1 x x^2 x^3 x^4 x^5 x^6 x^7 for
- ---------------------------------------------------------------
- 1 0 0 0 0 0 0 0
- . 1 0 0 0 0 0 0 (x+1)-1
- . . 1 1/2 1/3 1/12 3/40 -1/120 (x+1)^(x+1)-(x+1)
- . . . 1 1 17/12 5/4 469/360 (x+1)^(x+1)^(x+1)-(x+1)^(x+1)
- . . . . 1 3/2 11/4 31/8
- . . . . . 1 2 13/3
- . . . . . . 1 5/2
- . . . . . . . 1
- . . . . . . . 0
- exp(-lambertw(-log(1+x)))-1 \ Pari/GP gives the limiting set of
- \ coefficients for the infinite iteration height
- %20 = x + x^2 + 3/2*x^3 + 7/3*x^4 + 4*x^5 + 283/40*x^6 + 4681/360*x^7 + O(x^8)
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