A036056 Sum of the lengths of the cycle types of the permutation created by length sorting on the partitions of n.

1, 1, 1, 3, 3, 7, 11, 20, 25, 37, 54, 74, 98, 131, 169, 227, 293, 380, 486, 622, 787, 970, 1251, 1569, 1946, 2431, 3003, 3713, 4544, 5599