Logarithm of binomial series: Extension of a series of Knuth

Wenchang Chu

Abstract


The Lagrange expansion formula is employed to determine the Maclaurin series for the logarithms of Lambert’s series of binomial coefficients, extending the log–squared of the Catalan generating function due to Knuth (2015).

Keywords


Catalan numbers, Harmonic numbers, Elementary symmetric function, Bell polynomial, Lagrange expansion formula.

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ISSN: 1331-0623 (Print), 1848-8013 (Online)