  Ramanujan stated an identity to the effect that if three sequences $\{a_n\}$,
$\{b_n\}$ and $\{c_n\}$ are defined by $r_1(x)=:\sum_{n=0}^{\infty}a_nx^n$,
$r_2(x)=:\sum_{n=0}^{\infty}b_nx^n$ and $r_3(x)=:\sum_{n=0}^{\infty}c_nx^n$
(here each $r_i(x)$ is a certain rational function in $x$), then \[
a_n^3+b_n^3-c_n^3=(-1)^n, \hspace{25pt} \forall \,n \geq 0. \] Motivated by
this amazing identity, we state and prove a more general identity involving
eleven sequences, the new identity being "more general" in the sense that
equality holds not just for the power 3 (as in Ramanujan's identity), but for
each power $j$, $1\leq j \leq 5$.
