226 A Note on a Formula of Riordan Involving Harmonic Numbers J. A. Alonso-Carreón 1 , J. López-Bonilla 1a , Gyan Bahadur Thapa 2 1 ESIME-Zacatenco, Instituto Politécnico Nacional, Edif. 5, 1er. Piso, Col. Lindavista CP 07738, CDMX, México 2 Department of Applied Sciences, Pulcowk Campus, Institute of Engineering Tribhuvan University, Nepal a Corresponding author: jlopezb@ipn.mx Received: Oct 10, 2018 Revised: Dec 28, 2018 Accepted: Jan 2, 2019 Abstract: We employ Stirling numbers of the second kind to prove a relation of Riordan involving harmonic numbers. Keywords: Stirling numbers, Geometric series, Riordan’s identity, Harmonic numbers . 1. Introduction We know the Riordan’s relation [7]:       ൌͳ −  ൌ       ൌͳ ሺ−ͳሻ   ǡ ∀ℂǡ (1) for the harmonic numbers [6]:   ൌ  ͳ    ൌͳ Ǥ (2) It is usual to show (1) employing the geometric series and the binomial theorem of Newton; we observe that Agoh [1] also obtained this identity of Riordan. In Section 2, we exhibit an alternative proof of (1) via Stirling numbers [6, 7]. 2. Riordan’s formula The generating function for the Stirling numbers of the second kind is given by [6]:     Ǩ ∞  ൌ   ሾ ሿ ൌ ͳ  Ǩ ሺ  − ͳሻ  ǡ (3) with the property [3, 2]: cl Journal of the Institute of Engineering January 2019, Vol. 15 (No. 1): 226-228 © TUTA/IOE/PCU, Printed in Nepal TUTA/IOE/PCU