Moderate# Find Product of First Four Nonzero Coefficients of Power Series

MVCALC-1GOEMO

Find the product of the first four nonzero coefficients of the power series solution to:

$$(2x+1) y'' - y' + xy = 0, \quad y(0) = 1 \quad y'(0) = 2$$

...centered at $x_0 = 0$.