Great free softwares for an experimental (or whatever) mathematician:
Sagemath : Perhaps the best free CAS
J : An array programming language
FriCAS : Has some very good sequence guessing routines
ARPREC : "The Experimental Mathematician's Toolkit"
and here is a list of books:
Analytic combinatorics by Flajolet and Sidgewick.
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Last seen Jul 24 at 13:13