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We present several sequences involving harmonic numbers and the centralbinomial coefficients. The calculational technique is consists of a specialsummation method that allows, based on proper two-valued integer functions, tocalculate different families of power series which involve odd harmonic numbersand central binomial coefficients. Furthermore it is shown that based on theseseries a new type of nonlinear Euler sums that involve odd harmonic numbers canbe calculated in terms of zeta functions.

On four families of power series involving harmonic numbers and central binomial coefficients