Triangle T(n,k) = Sum_{i=1..n} 2^(i-1)*C(n+2*k-i-1, k-1), 1 <= k <= n.

Terms

a(0) =1a(1) =3a(2) =10a(3) =7a(4) =25a(5) =91a(6) =15a(7) =56a(8) =210a(9) =792a(10) =31a(11) =119a(12) =456a(13) =1749a(14) =6721a(15) =63a(16) =246a(17) =957a(18) =3718a(19) =14443a(20) =56134a(21) =127a(22) =501a(23) =1969a(24) =7722a(25) =30251a(26) =118456a(27) =463828a(28) =255a(29) =1012