| Title:
|
On some $q$-generalization of Super Catalan numbers (English) |
| Author:
|
Halıcı, Serpil |
| Author:
|
Gür, Zehra Betül |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
3 |
| Year:
|
2026 |
| Pages:
|
495-504 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of this paper is to generalize the Super Catalan numbers $S(m,n)$ and some properties of them by virtue of $q$-Calculus. For this purpose, we focus on formulating several weighted sums and different representations of the Super Catalan number sequence. Moreover, we derive some $q$-identities involving the $q$-Super Catalan numbers as a generalization of the results obtained for the numbers $S(m,n)$. (English) |
| Keyword:
|
binomial coefficient |
| Keyword:
|
Catalan numbers, Super Catalan numbers, $q$-identity |
| MSC:
|
05A10 |
| MSC:
|
11B65 |
| MSC:
|
11B83 |
| DOI:
|
10.21136/MB.2025.0166-24 |
| . |
| Date available:
|
2026-08-24T07:53:42Z |
| Last updated:
|
2026-08-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153719 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
