1995, with N. J. A. Sloane*The Encyclopedia of Integer Sequences*.

What comes next in the sequence 0, 1, 2? How about 720! (720
factorial)? Because 0 = 0, 1! = 1, 2!! = 2, so next comes 3!!! = 6!! =
720!. This little party trick example must be one of the few sequences
*not* listed in this wonderful book (although it does have the
sequence *n*!!).

*The Encyclopedia of Integer Sequences* is a revised and
updated version of the 1973 edition *A Handbook of Integer
Sequences*. It lists over 5000 sequences, in numerical order, each
with a brief cryptic description, and a cross-reference to the
literature where more information can be found. Most sequences are
shown to well over ten terms: given the number of sequences in the
book, that many terms can be needed to distinguish different ones! A
typical entry is:

From Euclid's proof. Ref GN75. BICA 8 27 93. [0,1; A5265]

Most of these sequences are of genuine mathematical interest (Fibonacci sequence, Catalan numbers, polynomial expansions, primes, continued fractions, to name but a few) or physical interest (magnetisation and susceptibility for square and cubic lattices, atomic weights) -- a few are just for fun (number of letters if written in Roman numerals). There is even a table, Figure M4822, of 'puzzle sequences' that aren't in the main body because they don't satisfy the rules for inclusion: (mostly) infinite integer sequences. The long list of sequences is leavened with the occasional diagram showing a geometrical interpretation of a particular sequence.

If you have generated a few terms of a sequence, and want to see if anything is known about it, then this is the essential reference (or you could try Sloane's On-Line Encyclopedia of Integer Sequences version). Even if you haven't got a particular sequence to track down, but are interested in number patterns, this makes for fascinating (and surprisingly addictive!) browsing.