24.4 Basic Properties24.6 Explicit Formulas

§24.5 Recurrence Relations

Contents

§24.5(i) Basic Relations

§24.5(ii) Other Identities

24.5.6 \sum _{{k=2}}^{n}{n\choose k-2}\frac{\mathop{B_{{k}}\/}\nolimits}{k}=\frac{1}{(n+1)(n+2)}-\mathop{B_{{n+1}}\/}\nolimits, n=2,3,\dots,
24.5.7 \sum _{{k=0}}^{n}{n\choose k}\frac{\mathop{B_{{k}}\/}\nolimits}{n+2-k}=\frac{\mathop{B_{{n+1}}\/}\nolimits}{n+1}, n=1,2,\dots,
24.5.8 \sum _{{k=0}}^{n}\frac{2^{{2k}}\mathop{B_{{2k}}\/}\nolimits}{(2k)!(2n+1-2k)!}=\frac{1}{(2n)!}, n=1,2,\dots.

§24.5(iii) Inversion Formulas

In each of (24.5.9) and (24.5.10) the first identity implies the second one and vice-versa.