a(n) = max T(n,k), with T as in A037027.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =10a(5) =22a(6) =51a(7) =111a(8) =256a(9) =594a(10) =1324a(11) =3130a(12) =7285a(13) =16435a(14) =39430a(15) =91959a(16) =211519a(17) =506408a(18) =1182650a(19) =2760810a(20) =6592080a(21) =15409740a(22) =36369225a(23) =86666790a(24) =202738635a(25) =482548825a(26) =1148125550a(27) =2687285975a(28) =6439167735a(29) =15301850850