The Electronic Journal of Combinatorics

v18i2p11 — Comment by the author, Jun 18, 2011.

Conjecture 10 was already made, in an equivalent form, in Section 5 of Zeilberger's paper [11] . Moreover, the conjecture has been proved by Krattenhaler in "Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions", (Electron. J. Combin. 4(1) (1997), #R27.). The determinants on page 8 are special cases of Theorems 30 and 31 in "Advanced Determinant Calculus" by Krattenhaler, Séminaire Lotharingien Combin. 42 (1999), Article B42q.