a(n) = Sum_{k=1..n} binomial(2*n - 3*k + 1, n - k)*k/(n - k + 1).

Terms

a(0) =0a(1) =1a(2) =3a(3) =6a(4) =11a(5) =23a(6) =60a(7) =182a(8) =589a(9) =1960a(10) =6641a(11) =22849a(12) =79676a(13) =281048a(14) =1001100a(15) =3595865a(16) =13009663a(17) =47366234a(18) =173415160a(19) =638044198a(20) =2357941155a(21) =8748646416a(22) =32576869239a(23) =121701491725a(24) =456012458960