The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
G.f.: A(x) = 1 + Sum_{n>=1} (1/n!)*Product_{j=0..n-1} L(2^j*x) where L(x) satisfies: x-x^2 = Sum_{j>=1}(1-2^j*x)*Prod_{i=0..j-1}L(2^i*x); and L(x) equals the g.f. of column 0 of the matrix log of A111975 (A111979).