Consider the Second-Order Differential Equation $\neq$ 0
Which of These Is the Explicit Formula for the of Frobenius

Consider the second-order differential equation .
Suppose the method of Frobenius is used to determine a power series solution of this equation. The indicial equation has r = 0 as a double root. So, one of the solutions can be represented as the power series .
Assume a₀ $\neq$ 0.
Which of these is the explicit formula for the coefficients ?

A) $a_{2 n}=\frac{(-1) ^{n} 2^{3 n}}{n !} a_{0, n} \geq 1$
B) $a_{2 n}=\frac{(-1) ^{n} 2^{5 n}}{n !} a_{0}, n \geq 1$
C) $a_{2 n}=\frac{(-1) ^{n} 2^{3 n}}{(n !) ^{2}} a_{0}, n \geq 1$
D) $a_{2 n}=\frac{(-1) ^{n} 2^{5 n}}{(n !) ^{2}} a_{0}, n \geq 1$