On New Sequences of $p$-Binomial and Catalan Transforms of the $k$-Mersenne Numbers and Associated Generating Functions
In this work, we investigate the binomial transforms and Catalan transform of the $k$-Mersenne and $k$-Mersenne-Lucas numbers and examine the new integer sequences. We apply the $p$-binomial, rising $p$-binomial, and falling $p$-binomial transforms to the $k$-Mersenne sequences and present the assoc...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2025-06-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/4614774 |
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| Summary: | In this work, we investigate the binomial transforms and Catalan transform of the $k$-Mersenne and $k$-Mersenne-Lucas numbers and examine the new integer sequences. We apply the $p$-binomial, rising $p$-binomial, and falling $p$-binomial transforms to the $k$-Mersenne sequences and present the associated generating and exponential generating functions for these transforms. Lastly, we provide the corresponding Binet-type formulas and recurrence relations for binomial transforms of the $k$-Mersenne ($k$-Mersenne-Lucas) numbers. These results are supported by numerical illustrations. |
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| ISSN: | 2619-9653 |