Number of non-isomorphic multiset partitions of weight n into singletons or strict pairs.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =13a(5) =23a(6) =55a(7) =104a(8) =236a(9) =470a(10) =1039a(11) =2140a(12) =4712a(13) =9962a(14) =21961a(15) =47484a(16) =105464a(17) =232324a(18) =521338a(19) =1167825a(20) =2651453a(21) =6031136a(22) =13863054a(23) =31987058a(24) =74448415a(25) =174109134a(26) =410265423a(27) =971839195a(28) =2317827540a(29) =5558092098