Add to ORKGWe prove that for any k = 1, . . . , 2n the 2-adic order of the Stirling number S(2n, k) of the second kind is exactly d(k) − 1, where d(k) denotes the number of 1’s among the binary digits of k. This confirms a conjecture of Lengyel.status: publishe
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers wi...
In the paper, the authors find two closed forms involving the Stirling numbers of the second kind an...
AbstractIn this paper, we prove some identities for the alternating sums of squares and cubes of the...
AbstractLet rs(n) denote the number of representations of n as the sum of s squares of integers. In ...
In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the firs...
By means of the connection coefficient approach, disjoint convolution sums are evaluated in closed f...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractIn this paper we give a modified approach to the generalized Stirling numbers of the second ...
AbstractThe n-th product level of a skew–field D, psn(D), is a generalization of the n-th level of a...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractFor m>n≥0 and 1≤d≤m, it is shown that the q-Euler number E2m(q) is congruent to qm−nE2n(q)mo...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
AbstractThe refined Stirling numbers of the first kindnm0m1 ··· mk−1 specify the number of permutati...
AbstractUsing the WZ-method we find some of the easiest Ramanujan's formulae and also some new inter...
AbstractBy using the Newton interpolation formula, we generalize the recent identities on the Catala...
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers wi...
In the paper, the authors find two closed forms involving the Stirling numbers of the second kind an...
AbstractIn this paper, we prove some identities for the alternating sums of squares and cubes of the...
AbstractLet rs(n) denote the number of representations of n as the sum of s squares of integers. In ...
In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the firs...
By means of the connection coefficient approach, disjoint convolution sums are evaluated in closed f...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractIn this paper we give a modified approach to the generalized Stirling numbers of the second ...
AbstractThe n-th product level of a skew–field D, psn(D), is a generalization of the n-th level of a...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractFor m>n≥0 and 1≤d≤m, it is shown that the q-Euler number E2m(q) is congruent to qm−nE2n(q)mo...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
AbstractThe refined Stirling numbers of the first kindnm0m1 ··· mk−1 specify the number of permutati...
AbstractUsing the WZ-method we find some of the easiest Ramanujan's formulae and also some new inter...
AbstractBy using the Newton interpolation formula, we generalize the recent identities on the Catala...
AbstractIn this paper we obtain an improved asymptotic formula on the frequency of k-free numbers wi...
In the paper, the authors find two closed forms involving the Stirling numbers of the second kind an...
AbstractIn this paper, we prove some identities for the alternating sums of squares and cubes of the...