Number of ways to select a set partition, P of {1,2,...,n} and then select a subset, S of {1,2,...,n} such that for all i in {1,2,...,n-1} if i and i+1 are in S then i and i+1 are in different blocks of P.

A227119

Number of ways to select a set partition, P of {1,2,...,n} and then select a subset, S of {1,2,...,n} such that for all i in {1,2,...,n-1} if i and i+1 are in S then i and i+1 are in different blocks of P.