Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a class of sequences defined by triangular recurrence equations. This class contains Stirling numbers and Eulerian numbers of both kinds, and hypergeometric multiples of those.  give a sufficient criterion for sums over such sequences to obey a recurrence equation, and present algorithms for computing such recurrence equations efficiently. Our algorithms can be used for verifying many known summation identities on Stirling numbers instantly, and also for discovering new identities.
['Manuel Kauers']
I am writing a research paper on a idea Summation algorithms for Stirling number identities
[{"from": "human", "value": "I am writing a research paper on a idea Summation algorithms for Stirling number identities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider a class of sequences defined by triangular recurrence equations. This class contains Stirling numbers and Eulerian numbers of both kinds, and hypergeometric multiples of those.  give a sufficient criterion for sums over such sequences to obey a recurrence equation, and present algorithms for computing such recurrence equations efficiently. Our algorithms can be used for verifying many known summation identities on Stirling numbers instantly, and also for discovering new identities."}]