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G.f. of reciprocals: R(x) = Sum_{n>=0} x^n/a(n) satisfies (1 + x) * R(x) = 1 + 2 * x * R'(x). - Werner Schulte, Nov 04 2024
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G.f. of reciprocals: AR(x) = Sum_{n>=0} x^n/a(n) satisfies (1+x) * AR(x) = 1 + 2 * x * AR'(x). - Werner Schulte, Nov 04 2024
RG.f.: A(x) = Sum_{n>=0} x^n / a(n) satisfies (1+x) * RA(x) = 1 + 2 * x * RA'(x), where R' is first derivative of R. - Werner Schulte, Nov 04 2024
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R(x) = Sum_{n>=0} x^n / a(n) satisfies (1+x) * R(x) = 1 + 2 * x * R'(x), where R' is first derivative of R. - Werner Schulte, Nov 04 2024
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a(n) = the number of relaxed compacted binary trees of right height at most one of size n. A relaxed compacted binary tree of size n is a directed acyclic graph consisting of a binary tree with n internal nodes, one leaf, and n pointers. It is constructed from a binary tree of size n, where the first leaf in a post-order traversal is kept and all other leaves are replaced by pointers. These links may point to any node that has already been visited by the post-order traversal. The right height is the maximal number of right-edges (or right children) on all paths from the root to any leaf after deleting all pointers. The numer number of unbounded relaxed compacted binary trees of size n is A082161(n). See the Genitrini et al. link. - Michael Wallner, Jun 20 2017
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