Taylor series related to one in Ramanujan's Lost Notebook.

Terms

a(0) =1a(1) =2a(2) =4a(3) =6a(4) =10a(5) =16a(6) =25a(7) =38a(8) =58a(9) =84a(10) =122a(11) =174a(12) =244a(13) =338a(14) =465a(15) =630a(16) =850a(17) =1136a(18) =1508a(19) =1988a(20) =2608a(21) =3398a(22) =4408a(23) =5688a(24) =7306a(25) =9342a(26) =11900a(27) =15090a(28) =19070a(29) =24008