  The "strange" function of Kontsevich and Zagier is defined by
\[F(q):=\sum_{n=0}^\infty(1-q)(1-q^2)\dots(1-q^n).\] This series is defined
only when $q$ is a root of unity, and provides an example of what Zagier has
called a "quantum modular form." In their recent work on congruences for the
Fishburn numbers $\xi(n)$ (whose generating function is $F(1-q)$), Andrews and
Sellers recorded a speculation about the polynomials which appear in the
dissections of the partial sums of $F(q)$. We prove that a more general form of
their speculation is true. The congruences of Andrews-Sellers were generalized
by Garvan in the case of prime modulus, and by Straub in the case of prime
power modulus. As a corollary of our theorem, we reprove the known congruences
for $\xi(n)$ modulo prime powers.

Number Theory;Combinatorics