Antoine Genitrini has pointed out the sage.combinat.combination algorithm which have originated from a MSDN blog post authored by James McCaffrey.

The sageMath algorithm can be found in our archive swh:1:cnt:c60366bc03936eede6509b23307321faf1035e23;origin=https://github.com/sagemath/sage;lines=473-537

In the code James McCaffrey is mentioned as the creator of the algorithm with a reference to his blog post which is difficult to find.

Here are some newer options:
https://msdn.microsoft.com/en-us/magazine/mt830362 => link rot
https://jamesmccaffrey.wordpress.com/2018/06/26/quick-generation-of-a-combination-element-using-the-combinadic-with-python/ => not archived in wayback machine, I fixed that
https://visualstudiomagazine.com/articles/2012/08/01/biginteger-data-type.aspx => still works and archived in wayback machine

There are sources on the blog page to download (with no license).
This sources (which are zip files) will be lost when the page will be lost.