a(n) = Sum_{m=0..n} Sum_{i=0..m} i*C(m-i,i)*C(m-i,n-m-i).

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =7a(5) =17a(6) =40a(7) =90a(8) =198a(9) =430a(10) =922a(11) =1956a(12) =4115a(13) =8597a(14) =17853a(15) =36883a(16) =75856a(17) =155396a(18) =317228a(19) =645580a(20) =1310132a(21) =2652072a(22) =5356277a(23) =10795351a(24) =21716195a(25) =43608549a(26) =87429944a(27) =175025918a(28) =349901074a(29) =698604058