f(n) = 1! + 2! + ... + n!

(姚脸)

这是常见版：
f(n) = {int sum=0,t=1;for(int i=1;i<=n;++i){t*=i;sum+=t;};return sum;}
这是标准版：
f(1) = 1!
f(Succ(n)) = f(n) + Succ(n)!
0! = 1
Succ(n)! = Succ(n)*n!
x*1 = x
x*Succ(n) = x*n + x
x+0 = x
x+Succ(n) = Succ(x) + n
这是原始递归版：
f(1) = g(1)
f(Succ(n)) = g(n, f(n))
g(x, y) = add(h(x, y), Proj2,2(x,y))
h(x, y) = i(Proj2,1(x,y))
i(n) = fact(Succ(n))
fact(1) = 1
fact(Succ(n)) = j(n, fact(n))
j(x, y) = mul(k(x, y), Proj2,2(x,y))
k(x, y) = Succ(Proj2,1(x,y))
add(x, 0) = Proj2,1(x, y)
add(x, Succ(y)) = l(x, add(x, y))
l(x, y) = Succ(Proj2,2(x,y))
mul(x, 0) = Zero2(x,0)
mul(x, Succ(y)) = m(x, mul(x, y))
m(x, y) = add(x, y)
这是数学：
f(n) = -1+(i π)/e+(Ei(1))/e-((-1)^n Γ(2+n) Γ(-1-n, -1))/e

(暴走)

ps. 不清楚算对了没...