Number of non-averaging permutations of [n] with first element ceiling(n/2).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =13a(7) =32a(8) =51a(9) =76a(10) =161a(11) =386a(12) =903a(13) =2280a(14) =5018a(15) =12828a(16) =19720a(17) =27656a(18) =48788a(19) =100120a(20) =220686a(21) =537208a(22) =1258242a(23) =3123166a(24) =7056165a(25) =17189752a(26) =35968308a(27) =82137764a(28) =189847917a(29) =509880208