Oh, Integrals ? How many ?

Taking a look at the first few terms in the sequence, we find this. $\int\int\text{ }dt\text{ }dt=\int t+C\text{ }dt=\dfrac{1}{2}t^2+Ct+D$ $\int\int\int\text{ }dt\text{ }dt\text{ }dt=\int\int t+C\text{ }dt\text{ }dt=\int\dfrac{1}{2}t^2+Ct+D\text{ }dt=\dfrac{1}{6}t^3+\dfrac{C}{2}t^2+Dt+F.$ It appears that the coefficient of the $n$ th term in the sequence is equal to a constant times the reciprocal of $n!$ In fact, the $n$ th term in the sequence is equal to this. $\dfrac{t^{n}}{n!}+\sum_{i=1}^{n-1}\dfrac{C_it^i}{i!}$ Because all constants are equal to $1,$ the $t^n$ term is equal to $\dfrac{t^n}{n!}$ with a coefficient of $\dfrac{1}{n!}$ .