Solving for variable inside a sum

Question

So a few calcuations have ultimately led me to this expression

$$ \sum_{n=1}^\infty \frac{B_n^2\left( \sinh\left( \sqrt 2\, \pi n \right) - \sqrt 2\,\pi n \right)}{4\pi\sqrt 2\, n} = 1 $$

Is there any way one can solve for $B_n$ in this case?

Answer 1

You can't if you don't make more assumptions.

All $B_n$ could be $0$ except one of them that would be whatever it takes to make the sum equal to $1$.

Or all $B_n$ except one could be anything at all such that the series converges, and the remaining $B_n$ whatever it takes to make the sum $1$.