T(n, k) = S(2n+2, n+2, k+2) for 0<=k<=n and n >= 0, array S as in A050157.

Terms

a(0) =1a(1) =3a(2) =4a(3) =9a(4) =14a(5) =15a(6) =28a(7) =48a(8) =55a(9) =56a(10) =90a(11) =165a(12) =200a(13) =209a(14) =210a(15) =297a(16) =572a(17) =726a(18) =780a(19) =791a(20) =792a(21) =1001a(22) =2002a(23) =2639a(24) =2912a(25) =2989a(26) =3002a(27) =3003a(28) =3432a(29) =7072