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We present several types of ordinary generating functions involving centralbinomial coefficients, harmonic numbers, and odd harmonic numbers. Our resultscomplement those of Boyadzhiev from 2012 and Chen from 2016. Based on thesegenerating functions we evaluate several infinite series in closed form. Inaddition, we offer some combinatorial sum identities involving Catalan numbers,harmonic numbers and odd harmonic numbers. Finally, we analyze a speciallog-integral with Fibonacci numbers and odd harmonic numbers.

Combinatorial sums, series and integrals involving odd harmonic numbers