In this little post I complete the details of the calculation
for the reciprocals , the famous so called Catalan numbers. It seems this is well known but it is scarcely quoted anywhere: Cf1, Cf2
We begin by recalling the relation , that is, in terms of the Beta function. So
This was hinted to me, thanks to, by the professor Qiaochu Yuan and I am not ashamed to confess that the calculations were executed in mathematica-v5. Why? well, the risk of introducing errors is a little-big.
ԩ` ͨ ˚ݤΥ`ѩ`ԩ`֥ɌTåפǤ֥ɥԩ`,`ѩ`ԩ`ڥߥեå⼤ͨ,ձNΥ֥ɷѥԩ`Ʒṩ¤nǤޤ,˚ݤΥ륤ȥԩ` åԩ`ץԩ`Щ`Х`ԩ`ԩ`ɥåͨʤ | AM11rޤǤΤעĤǵհk.
supreme ȥ ؔ ԩ`