Small challenge

[J-F Garnier]

Here is simple yet hopefully funny challenge.

A page at the HP Computer Museum shows this image of a HP 9835 screen, to demonstrate the quality of a restoration of the display:



The challenge is:

1 (easy): Can you find out the formula used to generate this series?

2 (more difficult): Can you find a HP 12-digit calculator that gives the very same and accurate results? Hint: a surprise here.
HP 12-digit calculator excludes the 10-digit machines (HP-41, Voyager) of course, but also the DM-42/Free42 and HP calculators in exact mode. True HP calculator emulators are welcome.

Math gurus would solve the part 1 almost immediately, but please refrain to spoil the game too quickly, until you can find which HP machine(s) can generate the very same 12-digit results for the series.

J-F