a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 + x^(3*k)))^n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =10a(4) =35a(5) =131a(6) =498a(7) =1919a(8) =7459a(9) =29170a(10) =114653a(11) =452552a(12) =1792754a(13) =7124040a(14) =28386081a(15) =113372690a(16) =453743907a(17) =1819317153a(18) =7306575042a(19) =29386858821a(20) =118348662525a(21) =477188876405