References
- Koshy T. Catalan numbers with applications. Oxford: Oxford University Press; 2009.
- Stanley RP. Catalan numbers. New York: Cambridge University Press; 2015. Available from: https://doi.org/10.1017/CBO9781139871495
- Kim DS, Kim T. A new approach to Catalan numbers using differential equations. Russ J Math Phys. 2017;24(4):487–496. Available from: https://doi.org/10.1134/S1061920817040070 doi: 10.1134/S1061920817040057
- Qi F. A simple form for coefficients in a family of ordinary differential equations related to the generating function of the Legendre polynomials. Adv Appl Math Sci. 2018;17(11):693–700.
- Qi F. Simplifying coefficients in a family of nonlinear ordinary differential equations. Acta Comment Univ Tartu Math. 2018;22(2):293–297. Available from: https://doi.org/10.12697/ACUTM.2018.22.24
- Qi F. Simplifying coefficients in a family of ordinary differential equations related to the generating function of the Laguerre polynomials. Appl Appl Math. 2018;13(2):750–755.
- Qi F. Simplifying coefficients in a family of ordinary differential equations related to the generating function of the Mittag–Leffler polynomials. Korean J Math. 2019;27(2):417–423. Available from: https://doi.org/10.11568/kjm.2019.27.2.417
- Qi F, Guo B-N. A diagonal recurrence relation for the Stirling numbers of the first kind. Appl Anal Discrete Math. 2018;12(1):153–165. Available from: https://doi.org/10.2298/AADM170405004Q
- Qi F, Guo B-N. Explicit formulas and recurrence relations for higher order Eulerian polynomials. Indag Math (NS). 2017;28(4):884–891. Available from: https://doi.org/10.1016/j.indag.2017.06.010
- Qi F, Lim D, Guo B-N. Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations. Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM. 2019;113(1):1–9. Available from: https://doi.org/10.1007/s13398-017-0427-2
- Qi F, Lim D, Guo B-N. Some identities related to Eulerian polynomials and involving the Stirling numbers. Appl Anal Discrete Math. 2018;12(2):467–480. Available from: https://doi.org/10.2298/AADM171008014Q
- Qi F, Liu A-Q, Lim D. Explicit expressions related to degenerate Cauchy numbers and their generating function. In: Singh J, Kumar D, Dutta H, Baleanu D, Purohit S, editors. Mathematical Modelling, Applied Analysis and Computation, ICMMAAC 2018. Springer Proceedings in Mathematics & Statistics, Vol. 272, Chapter 2, Singapore: Springer; p.41–52. Available from https://doi.org/10.1007/978-981-13-9608-3_2
- Qi F, Niu D-W, Guo B-N. Simplification of coefficients in differential equations associated with higher order Frobenius–Euler numbers. Tatra Mt Math Publ. 2018;72:67–76. Available from: https://doi.org/10.2478/tmmp-2018-0022
- Qi F, Niu D-W, Guo B-N. Simplifying coefficients in differential equations associated with higher order Bernoulli numbers of the second kind. AIMS Math. 2019;4(2):170–175. Available from: https://doi.org/10.3934/Math.2019.2.170
- Qi F, Niu D-W, Guo B-N. Some identities for a sequence of unnamed polynomials connected with the Bell polynomials. Rev R Acad Cienc Exactas Fís Nat Ser A Math RACSAM. 2019;113(2):557–567. Available from: https://doi.org/10.1007/s13398-018-0494-z
- Qi F, Zhao J-L. Some properties of the Bernoulli numbers of the second kind and their generating function. Bull Korean Math Soc. 2018;55(6):1909–1920. Available from: https://doi.org/10.4134/BKMS.b180039
- Qi F, Zou Q, Guo B-N. The inverse of a triangular matrix and several identities of the Catalan numbers. Appl Anal Discrete Math. 2019;13(2). Available from: https://doi.org/10.20944/preprints201703.0209.v2 doi: 10.2298/AADM171008014Q
- Zhao J-L, Wang J-L, Qi F. Derivative polynomials of a function related to the Apostol–Euler and Frobenius–Euler numbers. J Nonlinear Sci Appl. 2017;10(4):1345–1349. Available from: https://doi.org/10.22436/jnsa.010.04.06
- Comtet L. Advanced combinatorics: the art of finite and infinite expansions. Revised and Enlarged Edition. Dordrecht and Boston: D. Reidel Publishing Co.; 1974. Available from: https://doi.org/10.1007/978-94-010-2196-8
- Qi F, Guo B-N. Some properties and generalizations of the Catalan, Fuss, and Fuss–Catalan numbers. In: Ruzhansky Michael, Dutta Hemen, Agarwal Ravi P, editors. Mathematical analysis and applications: selected topics. 1st ed. Published by John Wiley & Sons, Inc. 2018. Chapter 5; p. 101–133. Available from: https://doi.org/10.1002/9781119414421.ch5
- Qi F, Shi X-T, Liu F-F, et al. Several formulas for special values of the Bell polynomials of the second kind and applications. J Appl Anal Comput. 2017;7(3):857–871. Available from: https://doi.org/10.11948/2017054
- Qi F, Niu D-W, Lim D. Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds. Miskolc Math Notes. 2019;21(1). https://doi.org/10.18514/MMN.2020.2976. doi: 10.18514/MMN.2019.2635
- Qi F, Qin X-L, Yao Y-H. The generating function of the Catalan numbers and lower triangular integer matrices. Preprints. 2017. 2017110120, 12 pages. Available from: https://doi.org/10.20944/preprints201711.0120.v1