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We consider the ground state energy of the Lieb-Liniger gas with $\delta$interaction in the weak coupling regime $\gamma\to0$. For bosons with repulsiveinteraction, previous studies gave the expansion$e_{\text{B}}(\gamma)\simeq\gamma-4\gamma^{3/2}/3\pi+(1/6-1/\pi^{2})\gamma^{2}$.Using a numerical solution of the Lieb-Liniger integral equation discretizedwith $M$ points and finite strength $\gamma$ of the interaction, we obtain veryaccurate numerics for the next orders after extrapolation on $M$ and $\gamma$.The coefficient of $\gamma^{5/2}$ in the expansion is found approximately equalto $-0.00158769986550594498929$, accurate within all digits shown. This valueis supported by a numerical solution of the Bethe equations with $N$ particlesfollowed by extrapolation on $N$ and $\gamma$. It was identified as$(3\zeta(3)/8-1/2)/\pi^{3}$ by G. Lang. The next two coefficients are alsoguessed from numerics. For balanced spin $1/2$ fermions with attractiveinteraction, the best result so far for the ground state energy was$e_{\text{F}}(\gamma)\simeq\pi^{2}/12-\gamma/2+\gamma^{2}/6$. An analoguedouble extrapolation scheme leads to the value $-\zeta(3)/\pi^{4}$ for thecoefficient of $\gamma^{3}$.

Ground state energy of the $\delta$-Bose and Fermi gas at weak coupling from double extrapolation