Result: On a combinatorial identity

Title:
On a combinatorial identity
Authors:
Gyires, B.
Source:
Publicationes Mathematicae Debrecen. 31:217-219
Publisher Information:
University of Debrecen/ Debreceni Egyetem, 2022.
Publication Year:
2022
Subject Terms:
asymptotic formula for Bernoulli numbers, calculation of Bernoulli numbers, recursive formulas, 0101 mathematics, Bernoulli and Euler numbers and polynomials, 01 natural sciences, Additive difference equations, Combinatorial identities, bijective combinatorics
Document Type:
Academic journal Article
File Description:
application/xml
ISSN:
0033-3883
DOI:
10.5486/pmd.1984.31.3-4.09
Access URL:
https://zbmath.org/3904664
Accession Number:
edsair.doi.dedup.....f465741dbbdaecb07046d8861fb053b2
Database:
OpenAIRE

Further Information

The author proves that the only solution of the difference equation \[ \Phi (2(v+1))+\sum^{v}_{k=1}\binom{2v}{2k-1} \Phi (2k) \Phi (2(v-k+1))=0 \] subject to the initial condition \(\Phi (2)=1/4\) is \(\Phi (2k)=((2^{2k}-1)/2k) B_{2k}\) where the \(B_{2k}\) are the even-indexed Bernoulli numbers. Using this result, he then proves that (1/k)\(| B_{2k}|^{1/2k}\to 1/\pi e\) as \(k\to \infty\).