关于二项系数和的递推公式

On Recurrences for Sums of Binomial Coefficients

Apery关于 ξ(3)是无理数的证明 ,极大地刺激了人们对于二项系数和序列的研究 。

It is well know that Apery sequence a n=∑nk=0n k 2n+k k 2 Satisfies a three terms polynomial recurrence for n≥1.The number theoretic properties of sums of bionomial coefficients have been studied by various people following the publication of Aper’s original proof.In this paper,we will show some results on the palynomial recurrences for sums of binomial coefficients.