Lattice paths and the Geode

Ira M. Gessel

Let $t_1,t_2,\dots$ be variables, and let $S$ be the formal power series in the variables $t_1,t_2,\dots$ satisfying $S=1+{\sum }_{i=1}^{\infty }{t}_n{S}^n.$ Let $S_1 =\sum_{n=1}^\infty t…