Number of set partitions of {1..n} where every block has the same average.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =5a(6) =5a(7) =18a(8) =16a(9) =75a(10) =64a(11) =405a(12) =302a(13) =2581a(14) =1693a(15) =19872a(16) =11295a(17) =175807a(18) =87524a(19) =1851135a(20) =787515a(21) =21909766a(22) =8185713a(23) =298698113a(24) =96514608a(25) =4538610230a(26) =1285072142a(27) =77584168396a(28) =19185810871a(30) =317348649579