Linear recurrence relations for sums of products of two terms (Q640425)

The author presents a general ansatz (covering as special cases Zeilberger's creative telescoping and Sister Celine's method) that guides one to search for recurrence relations of definite sums whose summands contain, e.g., Bernoulli numbers and Stirling numbers. This tactic is rather successful if one can split the summand into two multiplicative parts where one term satisfies a simple recurrence and depends on as few variables as possible. This allows to obtain a mildly coupled system whose solution produces a recurrence for the input sum. For special forms this approach turns out to be algorithmic.