SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2021 / Cilt: 45 - Sayı: 5

Explicit formulas and recurrence relations for generalized Catalan numbers

Muhammet Cihat DAĞLI
Pages
2171–2179
Publication Date
2022-11-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper, we present an explicit formula and recurrent relation for generalized Catalan numbers, from which we can give corresponding formulas for Schröder numbers, large and small generalized Catalan numbers for the special cases of our results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we present an explicit formula and recurrent relation for generalized Catalan numbers, from which we can give corresponding formulas for Schröder numbers, large and small generalized Catalan numbers for the special cases of our results.
📊
Key Findings & Data:In this paper, we present an explicit formula and recurrent relation for generalized Catalan numbers, from which we can give corresponding formulas for Schröder numbers, large and small generalized Catalan numbers for the special cases of our results.
💡
Conclusion & Impact:In this paper, we present an explicit formula and recurrent relation for generalized Catalan numbers, from which we can give corresponding formulas for Schröder numbers, large and small generalized Catalan numbers for the special cases of our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we present an explicit formula and recurrent relation for generalized Catalan numbers, from which we can give corresponding formulas for Schröder numbers, large and small generalized Catalan numbers for the special cases of our results.

🔖

Cite This Article

DAĞLI, M. C. (2022). Explicit formulas and recurrence relations for generalized Catalan numbers. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 5, 2171–2179. https://ajindex.com/articles/607370

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  1. Bourbaki N. Functions of a Real Variable, Elementary Theory. Translated from the 1976 French Original by Philip Spain. Elements of Mathematics (Berlin). Springer, Berlin: 2004
  2. Brualdi RA. Introductory Combinatorics. Fifth edition, Pearson Prentice Hall, Upper Saddle River, NJ: 2010
  3. Cao HQ, Pan H. A Stern-type congruence for the Schröder numbers. Discrete Mathematics 2017; 340: 708-712
  4. Chen Z, Pan H. Notes on the q−colored Motzkin numbers and Schröder numbers. Journal of Difference Equations and Applications 2017; 23 (6): 1133-1141
  5. Comtet L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, Revised and Enlarged Edition. D. Reidel Publishing Co., Dordrecht: 1974
  6. He TX. Parametric Catalan numbers and Catalan triangles. Linear Algebra and its Applications 2013; 438: 1467- 1484
  7. Koparal S, Ömür N. On congruences involving the generalized Catalan numbers and harmonic numbers. Bulletin of the Korean Mathematical Society 2019; 56: 649-658
  8. Koparal S, Ömür N. Some congruences involving Catalan, Pell and Fibonacci numbers. Mathematica Montisnigri 2020; 48: 10-18
  9. Koshy T. Catalan Numbers with Applications. Oxford University Press, Oxford: 2009
  10. Kruchinin DV, Kruchinin VV. Application of a composition of generating functions for obtaining explicit formulas of polynomials. Journal of Mathematical Analysis and Applications 2013; 404: 161-171
  11. Liu JC. A supercongruence involving Delannoy numbers and Schröder numbers. Journal of Number Theory 2016; 168: 117-127
  12. Liu JC. Proof of Sun’s conjectural supercongruence involving Catalan numbers. Electronic Research Archive 2020; 28 (2): 1023-1030
  13. Liu JC. On a congruence involving q−Catalan numbers. Comptes Rendus Mathématique 2020; 358: 211-215 [14] Liu JC, Huang ZY. A truncated identity of Euler and related q−congruences. Bulletin of the Australian Mathematical Society 2020; 102: 353-359
  14. Liu JC, Li L, Wang SD. Some congruences on Delannoy numbers and Schröder numbers. International Journal of Number Theory 2018; 14: 2035-2041
  15. Natalini P, Ricci PE. Higher order Bell polynomials and the relevant integer sequences. Applicable Analysis and Discrete Mathematics 2017; 11: 327-339
  16. Qi F. Parametric integrals, the Catalan numbers, and the beta function. Elemente Der Mathematik 2017; 72: 103-110
  17. Qi F, Akkurt A, Yildirim H. Catalan numbers, k-gamma and k-beta functions, and parametric integrals. Journal of Computational Analysis and Ap