Seems like (but needs checking that) $$\sum \frac{1}{\ell!} s(\ell,k) z^\ell t^k = \exp(t \sinh(z)).$$ That could probably be used to find other formulas, recurrences, etc.
Seems like (but needs checking that) $$\sum \frac{1}{\ell!} s(\ell,k) z^\ell t^k = \exp(t \sinh(z)).$$ That could probably be used to find other formulas, recurrences, etc.