Number of compositions of n such that any fixed point k can be k different colors.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =10a(5) =22a(6) =48a(7) =101a(8) =213a(9) =450a(10) =945a(11) =1961a(12) =4064a(13) =8385a(14) =17242a(15) =35332a(16) =72141a(17) =146924a(18) =298552a(19) =605377a(20) =1225277a(21) =2475912a(22) =4995754a(23) =10067848a(24) =20267680a(25) =40762951a(26) =81916919a(27) =164504411a(28) =330155437a(29) =662265817