2 problems

Let $R_k^B(n)$ denote the number of signed permutations of size $n$ whose burnt-pancake distance from the sorted stack is $k$. Summation identity conjecture. If $k,n\geq1$, then ……

Let $R_k^B(n)$ denote the number of signed permutations of size $n$ whose burnt-pancake distance from the sorted stack is $k$. Polynomial formulas conjecture. If $n\geq1$, then … ……