On Summing Formulas for Horadam Numbers

New formulas for Stirling-like numbers and Dobinski-like formulas

Extensions of the Stirling numbers of the second kind and Dobinski-like formulas are proposed in a series of exercises for graduetes. Some of these new formulas recently discovered by me are to be found in A.K.Kwaśniewski’s source paper [1]. These extensions naturally encompass the well known q-extensions.The indicatory references are to point at a part of the vast domain of the foundations of ...

Some Inversion Formulas and Formulas for Stirling Numbers

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

On the Product of Heights of Algebraic Numbers Summing to Real Numbers

Some Computational Formulas for D-Nِrlund Numbers

and Applied Analysis 3 It follows from 1.11 or 1.12 that t n, k t n − 2, k − 2 − 1 4 n − 2 t n − 2, k , 1.13 and that t n, 0 δn,0 n ∈ N0 : N ∪ {0} , t n, n 1 n ∈ N , t n, k 0 n k odd , t n, k 0 k > n or k < 0 , 1.14 where δm,n denotes the Kronecker symbol. By 1.13 , we have t 2n 1, 1 −1 n 2n ! 42n ( 2n n ) , t 2n 2, 2 −1 n n! 2 n ∈ N0 , 1.15 t 2n 2, 4 −1 n 1 n! 2 ( 1 1 22 1 32 · · · 1 n2 ) n ∈ ...

Explicit Formulas for Bernoulli and Euler Numbers

Explicit and recursive formulas for Bernoulli and Euler numbers are derived from the Faá di Bruno formula for the higher derivatives of a composite function. Along the way we prove a result about composite generating functions which can be systematically used to derive such identities.