Equations (24.5.3) and (24.5.4) enable and to be computed by recurrence. For higher values of more efficient methods are available. For example, the tangent numbers can be generated by simple recurrence relations obtained from (24.15.3), then (24.15.4) is applied. A similar method can be used for the Euler numbers based on (4.19.5). For details see Knuth and Buckholtz (1967).
Another method is based on the identities
For number-theoretic applications it is important to compute for ; in particular to find the irregular pairs for which . We list here three methods, arranged in increasing order of efficiency.