a(n) = Sum_{k=0..2n} (k+1) * A027082(n, 2n-k).

Terms

a(0) =1a(1) =6a(2) =20a(3) =62a(4) =188a(5) =566a(6) =1700a(7) =5102a(8) =15308a(9) =45926a(10) =137780a(11) =413342a(12) =1240028a(13) =3720086a(14) =11160260a(15) =33480782a(16) =100442348a(17) =301327046a(18) =903981140a(19) =2711943422a(20) =8135830268a(21) =24407490806a(22) =73222472420a(23) =219667417262a(24) =659002251788