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The type on the cover of theWest Barnum. However, it has unbracketed serifs, and the 'A' has no top bar.

Photo-Lettering's West Barnum Ultra, designed by Dave West and digitized by Ben Kiel & Adam Cruz, was film no. 5494 in the original Photo-Lettering archive. It arrives on Photo-Lettering with and without a shade. — House Industries

The ultra-heavy Western face was originally drawn in the 1960s. It is quite possible that there were variants and alternates.

There are two related but clearly weaker digital versions. One is PL Barnum Block, which is credited to Dave West, but — mainly due to more open counters in the uppercase and a looser spacing — doesn't have the same punch as West Barnum. The other one is Bolster, an all-caps variation with a few "biform" characters.

I assume the term Barnum is derived from circus pioneer P. T. Barnum (1810–1891). It is also used as the name of the corresponding style category on the Photo-Lettering website, where it collocates all kinds of Circus types.

Unrelated: Black Slabbath, "the heaviest typeface in the world".