Closed forms for derangement numbers in terms of the Hessenberg determinants

DOI10.1007/s13398-017-0401-zzbMath1401.05017OpenAlexW2560737759MaRDI QIDQ1800602

Feng Qi, Jiao-Lian Zhao, Bai-Ni Guo

Publication date: 24 October 2018

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-017-0401-z

zbMATH Keywords

derivativegenerating functionrecurrence relationclosed formHessenberg determinantderangement numbertridiagonal determinant

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Permutations, words, matrices (05A05) Recurrences (11B37) Special sequences and polynomials (11B83) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (14)

A new generalization of hyperharmonic numbers ⋮ Several closed and determinantal forms for convolved Fibonacci numbers ⋮ A new recursive formula arising from a determinantal expression for weighted Delannoy numbers ⋮ On a closed form for derangement numbers: an elementary proof ⋮ Study of degenerate derangement polynomials by \(\lambda\)-umbral calculus ⋮ Explicit, determinantal, recursive formulas and relations of the Peters polynomials and numbers ⋮ The deranged Bell numbers ⋮ Computation of several Hessenberg determinants ⋮ A diagonal recurrence relation for the Stirling numbers of the first kind ⋮ Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions ⋮ Some identities for a sequence of unnamed polynomials connected with the Bell polynomials ⋮ Unnamed Item ⋮ Several Determinantal Expressions of Generalized Tribonacci Polynomials and Sequences ⋮ Determinantal Formulas and Recurrent Relations for Bi-Periodic Fibonacci and Lucas Polynomials

Cites Work

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• Several closed expressions for the Euler numbers
• Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers
• Derivatives of tangent function and tangent numbers
• Two closed forms for the Bernoulli polynomials
• Inverse spectral problems for collections of leading principal submatrices of tridiagonal matrices
• Similarity reduction of a general matrix to Hessenberg form
• A Course in Enumeration
• Fibonacci Determinants
• A recovery of two determinantal representations for derangement numbers

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