The following conjectural "binomial" formula for the Jones polynomials

$$J(q)=(-1)^{n_-}q^{n_+-2n_-}\left(\sum_{k=0}^N\binom{N}{k}(-q)^k (q+1/q)^{\ell_{k+1}-1}\right)$$

is for a knot or link with $N$ crossings with a vector $\ell=[N,N-1,N-2,.....,2,1,2]$.

It is possible to write the following closed form

$$J(q) = (-1)^{n_-}q^{n_+-2n_-}{\frac {{q}^{-N+1}+ \left( -1 \right) ^{N}{q}^{N+1}+ \left( -1 \right) ^{N}{q} ^{N+3}+ \left( -1 \right) ^{N}{q}^{N-1} }{{q}^{2}+1}}$$

Such formula works well for the following knots : $3_1$, $5_1$, $7_1$, $9_1$, $K11a367$, $K13a4878$,...; and for the following links : $L2a1$, $L4a1$, $L6a3$, $L8a14$,...

My questions are:

What is the knot that follows after $K13a4878$ in the mentioned sequence? It must be a knot with $15$ crossings.

What is the link that follows after $L8a14$ in the mentioned sequence? It must be a link with $10$ crossings.

Do you think that the "binomial" formula is correct?

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