Binomial sums related to rational approximations to $\zeta (4)$

Wadim Zudilin

For the solution $\{u_n{\}}_{n=0}^{\infty }$ to the polynomial recursion $(n+1{)}^5{u}_{n+1}-3(2n+1)(3n^2+3n+1)(15n^2+15n+4)u_n-3n^3(3n-1)(3n+1)u_{n-1}=0$, where $n=1,2,...$, with the init…