Chapter 8.6, Problem 47E

To determine

(a)

To show:

The coefficients are given by the formula,

$a_k={15}^{7k}{a}_0/{\left(k!\right)}^9$, $k=0,1,2,\mathrm{...}$.

To determine

(b)

To find:

From the formula in part(a) with $a_0=1$, $a_5$, $a_{10}$, $a_{15}$, $a_{20}$ and $a_{25}$ and what the problem is.

To determine

(c)

To find:

Using the recurrence to compute $a_k$ for $k=1,2,3,\mathrm{...25}$ assuming $a_0=1$.

To determine

(d)

To state:

The advantage of recurrence relation over the formula.