Series with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers
نویسنده
چکیده
We present several generating functions for sequences involving the central binomial coefficients and the harmonic numbers. In particular, we obtain the generating functions for the sequences ( 2n n ) Hn, ( 2n n ) 1 nHn, ( 2n n ) 1 n+1Hn , and ( 2n n ) n m. The technique is based on a special Euler-type series transformation formula.
منابع مشابه
Interesting Series Associated with Central Binomial Coefficients, Catalan Numbers and Harmonic Numbers
We establish various generating functions for sequences associated with central binomial coefficients, Catalan numbers and harmonic numbers. In terms of these generating functions, we obtain a large variety of interesting series. Our approach is based on manipulating the well-known generating function of the Catalan numbers.
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