a(n) is the sum of products of terms in all partitions of n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =14a(5) =25a(6) =56a(7) =97a(8) =198a(9) =354a(10) =672a(11) =1170a(12) =2207a(13) =3762a(14) =6786a(15) =11675a(16) =20524a(17) =34636a(18) =60258a(19) =100580a(20) =171894a(21) =285820a(22) =480497a(23) =791316a(24) =1321346a(25) =2156830a(26) =3557353a(27) =5783660a(28) =9452658a(29) =15250216