Mathematica has a wide coverage of named functions defined by sums and recurrence relations. Often using original algorithms developed at Wolfram Research,
Mathematica supports highly efficient exact evaluation even for results involving millions of digits.
Fibonacci,
LucasL — Fibonacci and Lucas numbers and polynomials
BernoulliB — Bernoulli numbers and polynomials
NorlundB — Nörlund polynomials and generalized Bernoulli polynomials
EulerE — Euler numbers and polynomials
RecurrenceTable — create tables of values from recurrences and functional equations
RSolve — solve general recurrence relations
Sum — compute general finite and infinite sums
DifferenceRoot — symbolic representation of solutions to linear difference equations
FindSequenceFunction — find functional forms from sequences
