Number of derangements of S_n with exactly one peak.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =6a(5) =33a(6) =152a(7) =663a(8) =2778a(9) =11413a(10) =46332a(11) =186867a(12) =750878a(13) =3011025a(14) =12060480a(15) =48277423a(16) =193186146a(17) =772908429a(18) =3091983236a(19) =12368675691a(20) =49476275622a(21) =197908422985a(22) =791640682440