a(n) = n*Pell(n) * Sum_{d|n} 1/(d*Pell(d)) where Pell(n) = A000129(n).

Terms

a(0) =1a(1) =5a(2) =16a(3) =61a(4) =146a(5) =554a(6) =1184a(7) =4149a(8) =9457a(9) =29890a(10) =63152a(11) =222850a(12) =434994a(13) =1414642a(14) =3140576a(15) =9575893a(16) =19323714a(17) =65160959a(18) =125877072a(19) =408744626a(20) =865638272a(21) =2563647322a(22) =5176349664a(23) =17476326546a(24) =33019614771a(25) =102921708050a(26) =220209942688a(27) =657218691722