G.f. A(x) satisfies the condition that both A(x) and F(x) = A(x/F(x)) = o.g.f. of A157309 have zeros for every other coefficient after initial terms; g.f. of dual sequence A155585 satisfies the same condition.

A157310

G.f. A(x) satisfies the condition that both A(x) and F(x) = A(x/F(x)) = o.g.f. of A157309 have zeros for every other coefficient after initial terms; g.f. of dual sequence A155585 satisfies the same condition.