I want to know the Mathematica command for

$$f(a)=\sum_{n=0}^{a-1} \frac{f(n)}{n!}, \quad f(0)=1$$

How to write $f(0)=1$ together with the summation? I used:

Sum[f[a_ ]=f[n]/n!, {n,0,a-1}] , f(0)=1

Sum[f[a_ ]=f[n]/n!, {n,0,a-1}] // f(0)=1

but both didn't work

I know we can avoid writing $f(0)=1$ by separating the first term as

$$f(a)=1+\sum_{n=1}^{a-1}\frac{f(n)}{n!}$$

but I need the command without separation.

Thanks,

I want to know the Mathematica command for

$$f(a)=\sum_{n=0}^{a-1} \frac{f(n)}{n!}, \quad f(0)=1$$

How to write $f(0)=1$ together with the summation? I used:

Sum[f[a_ ]=f[n]/n!, {n,0,a-1}] , f(0)=1

Sum[f[a_ ]=f[n]/n!, {n,0,a-1}] // f(0)=1

but both didn't work

I know we can avoid writing $f(0)=1$ by separating the first term as

$$f(a)=1+\sum_{n=1}^{a-1}\frac{f(n)}{n!}$$

but I need the command without separation.

Thanks,