G.f.: exp( Sum_{n>=1} x^n/n * exp( Sum_{k>=1} Lucas(n*k)*x^(n*k)/k ) ) where Lucas(n) = A000032(n).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =16a(6) =36a(7) =64a(8) =135a(9) =250a(10) =504a(11) =917a(12) =1864a(13) =3372a(14) =6593a(15) =12176a(16) =23473a(17) =42732a(18) =82142a(19) =149282a(20) =283104a(21) =516780a(22) =967894a(23) =1757865a(24) =3291964a(25) =5959633a(26) =11039163a(27) =20022457a(28) =36908442a(29) =66637739