hello, (this is old material from 1993), I collected some of my notes about exact formulas for integer sequences. They are somewhat usefull since it can be used to compute the n'th term of a sequence. it uses [ ] , { } and some constants like exp(1). http://www.lacim.uqam.ca/%7Eplouffe/exact.htm note : most of those formulas do not appear in the current On-line Encyclopedia of integer sequences. By the way, can anybody do this : Can we find an EXACT formula for the n'th term of A001006 (Motzkin numbers), the only useful formula we have is a recurrence but with the index that grows with n which makes it difficult to compute for large n. http://www.research.att.com/projects/OEIS?Anum=A001006 is 1,1,2,4,9,21,51,127,323,835,2188,5798, ... and it grows roughly like 3^n. Simon Plouffe