calculating e value

Factorial Meaning, n! = 1×2×3×4…..(n-1)×n.

Factorial plusspluss n!++ = 1 x 2++ x 3++ x 4++ x … x (n-1)++ x n++;

1!++ = 1;

2!++ = 1 x 2++ = 3

3!++ = 3x 3++ = 9 + 1 = 10

4!++ = 10 x 4++ = 40 + 1 = 41

5!++ = 41 x 5++ = 205 + 1 = 206

6!++ = 206 x 6++ = 1236 + 1 = 1237

n!++ = (n-1)!++ x n + 1

note: add 1 to the product of a factorial except for 0 and 1;

e = 1 +  (n!++ /  n!);

We have n!  this needs to be redefined.

n! = 1 x 2 x 3 x 4 x 5 x ...  x n;

n!0 =  (((((((((( ((1 x 2) + 0) x 3) + 0) x 4) + 0) x 5) + 0) x 6) +
0) x n) + 0);

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all 0s are in a series like mi = m1 m2 ... mi

if we make this m sequence as {1,1,...,1}

then I name it as n!1

e = 1 + (n!1 / n!);
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e^x =  1 + (n!x^n / n!);

mi =  x^0, x^1, x^2,  x^3, x^4,  ....,  x^n

I am trying to calculate e^i value.

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note we may have to start from 2 or 3 for i some times depending on
the situation.