This is really more of a quasi-series that has some markings of a true series. To wit, despite using series numbers, 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 in late 1966. The earliest titles to receive this kind of series number seem to be H32 and H33, both out in Fall 1966. In 1967, Hill & Wang continued this number scheme, adding H34 in the spring and H35-H38 in the fall. Titles H39-H43 were added in the spring of 1968. The highest numbers I've come across in the wild have been H44 and H47, both issued Fall 1968.
In addition to these sequential numbers, Hill & Wang evidently added a few non-continuous numbers lower than H32 to what were likely later printings of earlier paperbacks. These seem to be retroactively numbered based on publication order of the original paperback editions. For example, William Mandel's Russia Re-Examined was first issued by Hill & Wang as a paperback at $1.95 in April 1964 but was later reissued in a revised paperback edition at $2.45 as H23 in the Fall 1967 list. Likewise, Elie Wiesel's Night was first issued by Hill & Wang as a paperback at $1.35 in the Fall 1964 list but was subsequently reissued, still at $1.35, with H25 on its spine (the copy I've found is designated a 3rd printing, but it's not clear when it was actually issued, though it's noted in a 1968 issue of Paperbound Books in Print.) The other example I've come across is Peace in Vietnam: A New Approach in Southeast Asia, first rushed to publication (see PW, Feb. 21, 1966, at 163) in April 1966 by Hill & Wang in paperback in 1966 at $.95. The following year a "New Enlarged Edition" was issued as HW31 at $1.25. There may be other such paperback reissues that follow the original paperback publication order, but these are the only three I've actually come across in the wild.
At some point, perhaps in 1968, Hill & Wang adopted SBNs, with the series book numbers being incorporated in the book number according to the format 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 to be used 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 later titles, as Hill & Wang abanonded using explicit series numbers 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.)