Several identities containing central binomial coefficients and derived from series expansions of powers of the arcsine function

Abstract

In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the Catalan numbers in combinatorial number theory.

Keywords

• identity
• product
• ratio
• central binomial coefficient
• power series expansion
• arcsine function
• square
• cubic
• generating function
• Catalan number

References

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