Arithmetic properties of coefficients of power series expansion of ${\prod }_{n=0}^{\infty }{\left(1-x^{2^n}\right)}^t$ (with an Appendix by Andrzej Schinzel)

Maciej Gawron, Piotr Miska, Maciej Ulas

Let $F(x)={\prod }_{n=0}^{\infty }(1-x^{2^n})$ be the generating function for the Prouhet-Thue-Morse sequence $((-1{)}^{s_2(n)}{)}_{n\in \mathbb{N}}$. In this paper we initiate the study of the…