a(n) = T(n,n) + T(n,n+1) + ... + T(n,2n), T given by A027113.

Terms

a(0) =1a(1) =3a(2) =9a(3) =27a(4) =79a(5) =231a(6) =672a(7) =1951a(8) =5662a(9) =16439a(10) =47776a(11) =139025a(12) =405110a(13) =1182107a(14) =3454035a(15) =10105373a(16) =29600389a(17) =86800887a(18) =254797772a(19) =748646741a(20) =2201587214a(21) =6479524339a(22) =19084115993a(23) =56246912653a(24) =165882843095a(25) =489509315203