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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.

Introduction to Probability

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