Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 9/7.

Terms

a(0) =1a(1) =3a(2) =5a(3) =8a(4) =13a(5) =22a(6) =39a(7) =69a(8) =120a(9) =206a(10) =353a(11) =607a(12) =1046a(13) =1803a(14) =3106a(15) =5348a(16) =9208a(17) =15856a(18) =27306a(19) =47025a(20) =80982a(21) =139457a(22) =240155a(23) =413566a(24) =712196a(25) =1226463a(26) =2112073a(27) =3637166a(28) =6263503a(29) =10786276