# 莱布尼茨三角形

L(r, 1) = 1rr為行編號，最小編號為1）
L(r, c) = |L(r − 1, c − 1) − L(r, c − 1)|c為為列編號，不會大於r

${\displaystyle {\begin{array}{cccccccccccccccccc}&&&&&&&&&1&&&&&&&&\\&&&&&&&&{\frac {1}{2}}&&{\frac {1}{2}}&&&&&&&\\&&&&&&&{\frac {1}{3}}&&{\frac {1}{6}}&&{\frac {1}{3}}&&&&&&\\&&&&&&{\frac {1}{4}}&&{\frac {1}{12}}&&{\frac {1}{12}}&&{\frac {1}{4}}&&&&&\\&&&&&{\frac {1}{5}}&&{\frac {1}{20}}&&{\frac {1}{30}}&&{\frac {1}{20}}&&{\frac {1}{5}}&&&&\\&&&&{\frac {1}{6}}&&{\frac {1}{30}}&&{\frac {1}{60}}&&{\frac {1}{60}}&&{\frac {1}{30}}&&{\frac {1}{6}}&&&\\&&&{\frac {1}{7}}&&{\frac {1}{42}}&&{\frac {1}{105}}&&{\frac {1}{140}}&&{\frac {1}{105}}&&{\frac {1}{42}}&&{\frac {1}{7}}&&\\&&{\frac {1}{8}}&&{\frac {1}{56}}&&{\frac {1}{168}}&&{\frac {1}{280}}&&{\frac {1}{280}}&&{\frac {1}{168}}&&{\frac {1}{56}}&&{\frac {1}{8}}&\\&&&&&\vdots &&&&\vdots &&&&\vdots &&&&\\\end{array}}}$

${\displaystyle L(r,c)=\int _{0}^{1}\!x^{c-1}(1-x)^{r-c}\,dx\,.}$

## 參考資料

1. ^ Crilly, Tony. 50 Mathematical Ideas you really need to know. London: Quercus. 2007: 53. ISBN 978-1-84724-008-8.
2. ^ Wells, David (1986). The Penguin Dictionary of Curious and Interesting Numbers, p.98. ISBN 978-0-14-026149-3.