Triangle of coefficients arising in study of up-down permutations.

Terms

a(0) =1a(1) =-2a(2) =1a(3) =6a(4) =-6a(5) =1a(6) =-23a(7) =36a(8) =-15a(9) =1a(10) =106a(11) =-229a(12) =160a(13) =-37a(14) =1a(15) =-567a(16) =1574a(17) =-1566a(18) =650a(19) =-93a(20) =1a(21) =3434a(22) =-11706a(23) =15248a(24) =-9310a(25) =2572a(26) =-238a(27) =1a(28) =-23137a(29) =93831