For integers $a\geq1$ and $b\geq1-a$, the series $C_{a,b}=\sum_{n=1}^{\infty} n!/((a+1)n+b)!$ is transcendental. Equivalently, the series in Erdős Problem 270 is transcendental whenever $f(n)=an+b$ is a positive integer-valued affine function.