This is really more of a quasi-series that has some markings of a true series. First, there's not really a name for the series: these are just paperbacks published by Hill & Wang. In keeping with their conventions for series like the Dramabooks and American Century, however, H&W apparently decided to add series numbers, with H- prefixes, to the spines of their paperbacks starting around late 1966. The earliest titles to receive this kind of series number seem to be H-32 and H-33, both out in Fall 1966. In 1967, Hill & Wang continued this number scheme, adding H-34 in the spring and H-35 through H-38 in the fall. Titles H-39 through H-43 were added in the spring of 1968. The highest numbers I've come across in the wild have been H-44 and H-47, both from Fall 1968.
In addition to these sequential numbers, Hill & Wang evidently added a couple non-continuous numbers to what were likely later printings of earlier titles. For example, H-31 shows up in Spring 1967 and H-23 in the fall of that year. It's apparent, based on the SBNs/ISBNs that Hill & Wang was publishing their paperbacks at this point with sequential book numbers with the format 0-8090-13xx-c. This is similar to how they handled the Dramabooks lines and the American Century series around 1968/1969. Although H-47 is the highest use of this series number I've seen, the numbers continued covertly within the book numbers, continuing at least as high as 0-8090-1399-1 in 1982. I don't see a point in listing out all these titles, as this is not really a series in the first place and any feints at making this a quasi-series were seemingly abandoned by Hill & Wang after 1968. As a result, I'm leaving off with the 1969 titles, which I examined to verify they didn't have series numbers on their spines (these titles have brackets around their series numbers, as they merely bear the suggestion of the numbers via their book numbers.)