algorithms – Some programming languages for Enumerative Combinatorics

I am master student in mathematics and i am new in computer science .I want to ask best and recent algorithms and approximations for the field of (Enumerative) Combinatorics in Computer Programming? For example like developing a new algorithm for stirling numbers ? or using algorithms for a special number? Maybe you have any other interesting ideas,too

I searched that there are C++ ,Java, Fortran, Pyton, Dynamic programming? Which one can i use it and why? Thank you for your answers and references.