a(n) = Sum_{k=0..n} (k+1) * A026725(n, n-k).

Terms

a(0) =1a(1) =3a(2) =8a(3) =23a(4) =55a(5) =144a(6) =328a(7) =816a(8) =1808a(9) =4358a(10) =9485a(11) =22377a(12) =48097a(13) =111720a(14) =237917a(15) =546161a(16) =1154827a(17) =2626624a(18) =5522464a(19) =12467540a(20) =26092324a(21) =58546544a(22) =122059348a(23) =272479782a(24) =566242186a(25) =1258568324a(26) =2608232758a(27) =5775620396a(28) =11940756076