Taikoban o Osu "to stamp a drum-size seal"

On official documents in Japan, a name-stamp is used rather than a signature. Seals vary in size and shape, but generally the bigger the seal, the greater the status. The seal for a university, for example, will be larger and more impressive-looking than the seal for an individual. Metaphorically, a "drum-size seal" is an enthusiastic endorsement, often used as a strong recommendation.