In this paper, we introduce a new type of generalized alternating hyperharmonic numbers H (p,r,s1,s2) n , and show that Euler sums of the generalized alternating hyperharmonic numbers H (p,r,s1,s2) n can be expressed in terms of linear combinations of classical (alternating) Euler sums.

In this paper, we give explicit asymptotic formulas for some sums over primes involving generalized alternating hyperharmonic numbers of types I, II and III. Analogous results for numbers with $k$-prime factors will also be considered.

In this paper, we mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.

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Convolution identities for various numbers (e.g., Bernoulli, Euler, Genocchi, Catalan, Cauchy and Stirling numbers) have been studied by many authors. Recently, several convolution identities have been studied for Fibonacci and Tribonacci numbers too. In this paper, we give convolution identities with and without binomial (multinomial) coefficients for Tetranacci numbers, and convolution identities with binomial coefficients for Tetranacci and Tetranacci-type numbers.