I had computed the values for n up to 8 long ago and reported them in a letter to the editor of the Journal of Recreational Mathematics 2 (1969), 155-157. The values for n=9 and n=10 are new, found using ZDDs.

For best known results see link to Alex Chernov's site. - Dmitry Kamenetsky, Mar 02 2021

REFERENCES

D. E. Knuth, Selected Papers on Fun and Games. CSLI, Stanford, CA, 2010. (CSLI Lecture Notes, vol. 192)