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We give a purely algebraic proof of a formula for Taylor coefficients of the reciprocal gamma function. The formula expresses each coefficient in terms of multiple zeta values. Our proof uses Hoffman’s harmonic algebra of multiple zeta values.
A $k$-Artal arrangement is a reducible algebraic curve composed of a smooth cubic and $k$ inflectional tangents. By studying the topological properties of their subarrangements, we prove that for $k=3,4,5,6$, there exist Zariski pairs of $k$-Artal arrangements. These Zariski pairs can be distinguished in a geometric way by the number of collinear triples in the set of singular points of the arrangement contained in the cubic.