The purpose of this paper is to find an explicit formula and asymptotic estimate for the total number of sum of weighted records over set partitions of $[n]$ in terms of Bell numbers. For that we study the generating function for the number of set partitions of $[n]$ according to the statistic sum of weighted records.
An explicit formula for the number of permutations with a given number of alternating runs
Cyclically consecutive permutation avoidance
On the number of partitions of $n$ whose product of the summands is at most $n$
![QR code for arXiv:1906.00680 [math.CO]](http://oss.arxitics.com/images/favicon.svg)