a(n) is the number of patterns for n-character papaya words in an infinite alphabet.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =10a(5) =21a(6) =50a(7) =99a(8) =250a(9) =454a(10) =1242a(11) =2223a(12) =6394a(13) =11389a(14) =35002a(15) =62034a(16) =202010a(17) =359483a(18) =1233518a(19) =2203507a(20) =7944110a(21) =14249736a(22) =53811584a(23) =96912709a(24) =382289362a(25) =691110821a(26) =2841057442a(27) =5154280744a(28) =22033974854a(29) =40105797777