[1] G. Alvarez, J. E. Bergner and R. Lopez, Action graphs and Catalan numbers, J. Integer Seq.,18 2015 pp. 7.
[2] H. Alzer and G. V. Nagy, Some identities involving central binomial coefficients and Catalan numbers, Integers, 20
2020 pp. 17.
[3] G. E. Andrews, On Shapiro’s Catalan convolution, Adv. Appl. Math., 46 (2011) 15–24.
[4] R. Apéry, Irrationalité de ζ(2) et ζ(3), Asterisqué, No. 61 (1979) 11–13.
[5] V. De Angelis, Pairings and signed permutations, Amer. Math. Monthly, 113 (2006) 642–644.
[6] K. Ball, MA241 Combinatorics, https://warwick.ac.uk/fac/sci/.
[7] J. M. Borwein and P. B. Borwein, Pi and the AGM: A study in Analytic Number Theory and Computational Complex-
ity, Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication.
John Wiley & Sons, Inc., New York, 1987.
[8] K. N. Boyadzhiev, Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Integer
Seq., 15 2012 pp. 11.
[9] J. M. Campbell, New series involving harmonic numbers and squared central binomial coefficients, Rocky Mountain
J. Math., 49 (2019) 2513–2544.
[10] G. Chang and C. Xu, Generalization and probabilistic proof of a combinatorial identity, Amer. Math. Monthly, 118
(2017) 175–177.
[11] H. Chen, Interesting series associated with central binomial coefficients, Catalan numbers and harmonic numbers,
J. Integer Seq., 19 (2016) pp. 11.
[12] R. Duarte and A. G. de Oliveira, A short proof of a famous combinatorial identity, (2013), http://arxiv.org/abs/
1307.6693.
[13] R. Duarte and A. G. Oliveira, A famous identity of Hajós in terms of sets, J. Integer Seq., 17 (2014) pp. 10.
[14] N. Elezović, Asymptotic expansions of central binomial coefficients and Catalan numbers, J. Integer Seq., 17 (2014)
pp. 14.
[15] P. Hajnal and G. V. Nagy, A bijective proof of Shapiro’s Catalan convolution, Electronic J. Combin., 21 (2014)
pp. 10.
[16] T. Kosby, Catalan numbers with applications, Oxford Univ. Press, Oxford, 2009.
[17] W.-H. Li, F. Qi, O. Kouba and I. Kaddoura, A further generalization of the Catalan number and its explicit formula
and integral representation, preprint, (2020), https://doi.org/10.31219/osf.io/zf9xu.
[18] T. Mansour, Y. Sun, Identities involving Narayana polynomials and Catalan numbers, Discrete Math., 309 (2009)
4079–4088.
[19] G. V. Nagy, A combinatorial proof of Shapiro’s Catalan convolution, Adv. Appl. Math., 49 (2012) 391–396.
[20] M. Petkovšek, H. S. Wilf and D. Zeilberger, A=B, A. K. Peters, Ltd., Wellesley, Mass., 1996.
[21] F.Qi, C.-P. Chen and D. Lim, Several identities containing central binomial coefficients and derived from series
expansions of powers of the arcsine function, Results in Nonlinear Analysis, 4 (2021) 57-64.
[22] F. Qi, Some properties of the Catalan numbers, Ars Combinatoria, in press, https://www.researchgate.net/
publication/328891537.
[23] F. Qi, W.-H. Li, J. Cao, D.-W. Niu,and J.-L. Zhao, An analytic generalization of the Catalan numbers and its
integral representation, preprint (2020), https:arxiv.org/abs/2005.13515v1.
[24] R. Sprugnoli, Sums of reciprocals of the central binomial coefficients, Integers, 6 (2006) pp. 18.
[25] H. M. Srivastava and J. Choi, Zeta and q–zeta Functions and Associated Series and Integrals, Elsevier, 2012.
[26] R. P. Stanley, Catalan Addendum, http://math.mit.edu/~rstan/ec/catadd.pdf.
[27] R. P. Stanley, Catalan Numbers, Cambridge Univ. Press, Cambridge, 2015.
[28] M. Sved, Counting and recounting, Math. intelligencer, 4 (1983) 21–26.
[29] M. Sved, Counting and recounting: The aftermath, Math. intelligencer, 6 (1984) 44–46.
[30] H. S. Wilf and D. Zeilberger, Rational functions certify combinatorial identities, J. Amer. Math. Soc., 3 (1990)
147–158.
[31] R. Witula, E. Hetmaniok, D. Slota and N. Gawrońska, Convolution identities for central binomial numbers, Int. J.
Pure Appl. Math., 85 (2013) 171–178.
)
