differential equations – Resolution of the recurrence relation for the expansion coefficients of the asymptotic expansion of an ODE

I want to solve the asymptotic solution of the following differential equation

$$ left (y ^ 2 + 1 right) R & # 39; (y) + y left (2 -p left (b_ {0} sqrt {y ^ 2 + 1} right) ^ {- p} right) R (## EQU1 ## + 1) R (y) = 0 $$

as $ y rightarrow infty $, or $ p> 0 $. I used the standard method in obtaining a serial solution according to the Frobenius method, in the form

$$ R (y) = sum_ {n = 0} ^ infty frac {a_ {n}} {y ^ {n + k}} $$
or $ k = l + 1 $ is the indicative exponent. I had trouble finding, by hand, a recurrence relation for the coefficients $ a_n $ for arbitrary value of the parameter $ p $. Right now, I'm only doing the brute force method of individual resolution $ a_n $ for each value of $ p $.

But I'm just wondering if the recurrence relation is possible to use with the Mathematica routine. Any help is appreciated.