G.f.: Product_{k>=1} 1/(1-x^k)^Fibonacci(k+2).

Terms

a(0) =1a(1) =2a(2) =6a(3) =15a(4) =38a(5) =89a(6) =210a(7) =474a(8) =1065a(9) =2339a(10) =5091a(11) =10919a(12) =23230a(13) =48887a(14) =102126a(15) =211599a(16) =435561a(17) =890617a(18) =1810786a(19) =3661118a(20) =7365473a(21) =14747049a(22) =29397160a(23) =58356179a(24) =115392801a(25) =227332038a(26) =446304671a(27) =873298579a(28) =1703463864a(29) =3312873935