The ditty is "To Anacreon in Heaven".
The men-only club was called The Anacreontic Society. Anacreon was a Sixth Century BCE Greek poet. The fragments of his poems that survive are devoted to wine, women, and song. Lyrics are here:

http://www.contemplator.com/america/anacreon.html

Caution: The MIDI file embedded in the website uses a high-pitched "flute".